The third edition of Webster’s International Dictionary, first published in 1961, represented a novel approach to lexicography. It recorded the English language used in everyday life, incorporating colloquial terms that previous grammarians would have considered unfit for any responsible dictionary. Many were scandalized by the new lexicography. Trademark lawyers were not the most prominent of these critics, but the concerns they expressed are significant because they touched on the core structure of the trademark as a form of property in (...) language. In the course of eavesdropping on everyday usage, Merriam-Webster’s lexicographers picked up on the use of trademarks as common nouns: “thermos” as a generic noun for any vacuum flask, “cellophane” as a term for transparent wrapping, and so on. If Webster’s Third were to be taken as sound evidence of the meaning of words, then the danger was that some of the most familiar marks in the USA would be judged “generic” in the legal sense, and would thereby cease to be proprietary. In this article, we explore the implications of this encounter between law and lexicographic technique. (shrink)

Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We (...) show that the theory of the generic model of $K_\alpha $ is AE-axiomatizable for any α. (shrink)

In this paper two new combinatorial principles in nonstandard analysis are isolated and applications are given. The second principle provides an equivalent formulation of Henson's isomorphism property.

Generics are sentences such as Birds fly, which express generalizations. They are prevalent in speech, and as far as is known, no human language lacks generics. Yet, it is very far from clear what they mean. After all, not all birds fly—penguins don’t! -/- There are two general views about the meaning of generics in the literature, and each view encompasses many specific theories. According to the inductivist view, a generic states that a sufficient number of individuals satisfy a (...) certain property—in the example above, it says that sufficiently many birds fly. This view faces the complicated problem of spelling out exactly how many is “sufficiently many” in a way that correctly captures the intuitive truth conditions of generics. -/- An alternative, the rules and regulations view, despairs from this project and proposes instead that generics directly express rules in the world. Rules are taken to be abstract objects, which are not related to the properties of specific individuals. This view faces the difficult problem of explaining how people come to know of such rules when judging the truth of falsity of generics, and accounting for the strong intuition that a sentence such as Birds fly talks about birds, not abstract objects. -/- What seems to be beyond dispute is that generics, even if they do not express rules, are lawlike: they state non-accidental generalizations. Many scholars have taken this fact to indicate that generics are parametric on possible worlds: they refer to worlds other than the actual world. This, again, raises the problem of how people come to know about what happens in these other worlds. However, a rigorous application of standard tests for intensionality shows that generics are not, in fact, parametric on possible worlds, but only on time. This unusual property may explain much of the mystery surrounding generics. -/- Another mysterious property of generics is that although there is no language without them, there is no linguistic construction that is devoted to the expression of genericity. Rather, generics can be expressed in a variety of ways, each of which can also express nongenerics. Yet, each manifestation of generics differs subtly (or sometimes not so subtly) in its meaning from the others. -/- Even when these and other puzzles of genericity are solved, one mystery would remain: Why are generics, which are so easy to produce and understand in conversation, so difficult to analyze? (shrink)

Consensus has it that generic sentences such as “Dogs bark” and “Birds fly” contain, at the level of logical form, an unpronounced generic operator: Gen. On this view, generics have a tripartite structure similar to overtly quantified sentences such as “Most dogs bark” and “Typically, birds fly”. I argue that Gen doesn’t exist and that generics have a simple bipartite structure on par with ordinary atomic sentences such as “Homer is drinking”. On my view, the subject terms of (...) generics are kind-referring. The interesting truth conditions characteristic of generics arise from the interesting ways in which kinds inherit properties from their members. (shrink)

Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T{“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T{“σi is an automorphism”: (...) i=1,2} is an elementary class if and only if T has the definable multiplicity property. (shrink)

Generics (e.g., “Ravens are black”) express generalizations about categories or their members. Previous research found that generics about animals are interpreted as broadly true of members of a kind, yet also accepted based on minimal evidence. This asymmetry is important for suggesting a mechanism by which unfounded generalizations may flourish; yet, little is known whether this finding extends to generics about groups of people (heretofore, “social generics”). Accordingly, in four preregistered studies (n = 665), we tested for an inferential asymmetry (...) for generics regarding novel groups of animals versus people. Participants were randomly assigned to either an Implied Prevalence task (given a generic, asked to estimate the prevalence of a property) or a Truth-Conditions task (given prevalence information, asked whether a generic was true or false). A generic asymmetry was found in both domains, at equivalent levels. The asymmetry also extended to properties varying in valence (dangerous and neutral). Finally, there were differences as a function of property valence in the Implied Prevalence task and a small but consistent interaction between domain and prevalence in the Truth-Conditions task. We discuss the implications of these results for the semantics of generics, theoretical accounts of the asymmetry, and the relation between generics and stereotyping. (shrink)

In his _Between Logic and the World_, in the course of presenting his theory of generics, Nickel (Between logic and the world, Oxford University Press, 2016) argues for a theory of characteristicness, or “genericity”, which states that a property is characteristic for a kind if and only if its presence among the members of that kind is explicable by some explanatory domain that recognizes the existence of that kind in the course of engaging the explanatory strategies made available by (...) that explanatory domain. I argue that this notion of genericity is too narrow, excluding properties characteristic for kinds that go unrecognized in such explanatory domains. In particular, Nickel’s theory excludes some characteristic properties of anthropic kinds, such as lilies and cedars, members of which have properties that may be similarly exploited in various human practices despite having divergent geneses. I argue for a generalization of Nickel’s view of genericity where explicability of presence is only one sort of genericity, with others, such as practicability, being possible too. (shrink)

Generic statements (e.g., “Birds lay eggs”) express generalizations about categories. In this paper, we hypothesized that there is a paradoxical asymmetry at the core of generic meaning, such that these sentences have extremely strong implications but require little evidence to be judged true. Four experiments confirmed the hypothesized asymmetry: Participants interpreted novel generics such as “Lorches have purple feathers” as referring to nearly all lorches, but they judged the same novel generics to be true given a wide range (...) of prevalence levels (e.g., even when only 10% or 30% of lorches had purple feathers). A second hypothesis, also confirmed by the results, was that novel generic sentences about dangerous or distinctive properties would be more acceptable than generic sentences that were similar but did not have these connotations. In addition to clarifying important aspects of generics’ meaning, these findings are applicable to a range of real-world processes such as stereotyping and political discourse. (shrink)

Access to medicines faces a new legal threat: “border enforcement” of drug patents. Using Brazil as an example, this article shows how the right to health depends on international trade. Border seizures of generic drugs present human rights and trade institutions with a unique challenge. Can public health advocates rise to meet it?

Most new drugs are protected by pharmaceutical patents, which give the patent holder exclusive control over that drug’s supply for 20 years. When the patent term expires, the drug becomes available for generic production by any company. The resulting competition typically leads to dramatic reductions in price. In Brazil, generic drugs are on average 40% cheaper than reference or brand-name drugs. In the United States, the Federal Drug Administration reports up to 85% price differences. Consumers in India have (...) witnessed more than 100-fold price reduction for antiretroviral drugs due to generic production. Generics thus play a key role in broadening access to health care, mostly by driving costs down, both in the developing and developed world. (shrink)

Generics are exception-admitting generalisations, which find expression in apparently diverse linguistic forms. A standard claim is that there is a hidden linguistic unity to genericity in the form of a covert operator, Gen. This article surveys and rejects a range of considerations that purport to show Gen to be syntactically essential to the explanation of a range of linguistic phenomena connected to genericity. The conclusion reached is that genericity is not a specifically linguistic property insofar as it does not (...) supervene upon any especial linguistic device; rather, genericity supervenes on broader cognitive competencies within linguistic constraints. (shrink)

Generic statements (‘Tigers have stripes’) are pervasive and early-emerging modes of generalization with a distinctive linguistic profile. Previous experimental work found that generics display a unique asymmetry between their acceptance conditions and the implications that are typically drawn from them. This paper presents evidence against the hypothesis that only generics display an asymmetry. Correcting for limitations of previous designs, we found a generalized asymmetry effect across generics, various kinds of explicitly quantified statements (‘most’, ‘some’, ‘typically’, ‘usually’), and variations in (...) types of predicated properties (striking vs. neutral). We discuss implications of these results for our understanding of the source of asymmetry effects and whether and in which ways these effects might introduce biased beliefs into social networks. (shrink)

If T is a model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.

The generic pronoun 'one' (or its empty counterpart, arbitrary PRO) exhibits a range of properties that show a special connection to the first person, or rather the relevant intentional agent (speaker, addressee, or described agent). The paper argues that generic 'one' involves generic quantification in which the predicate is applied to a given entity ‘as if’ to the relevant agent himself. This is best understood in terms of simulation, a central notion in some recent developments in the (...) philosophy of mind and cognitive science (Simulation Theory). (shrink)

Our knowledge about the world is often expressed by generic sentences, yet their meanings are far from clear. This book provides answers to central problems concerning generics: what do they mean? Which factors affect their interpretation? How can one reason with generics? Cohen proposes that the meanings of generics are probability judgments, and shows how this view accounts for many of their puzzling properties, including lawlikeness. Generics are evaluated with respect to alternatives. Cohen argues that alternatives are induced by (...) the kind as well as by the predicated property, and thus provides a uniform account of the varied interpretations of generics. He studies the formal properties of alternatives and provides a compositional account of their derivation by focus and presupposition. Cohen uses his semantics of generics to provide a formal characterization of adequate default reasoning, and proves some desirable results of this formalism. (shrink)

There is a standard quantificational view of generic sentences according to which they have a tripartite logical form involving a phonologically null generic operator called 'Gen'. Recently, a number of theorists have questioned the standard view and revived a competing proposal according to which generics involve the predication of properties to kinds. This paper offers a novel argument against the kind-predication approach on the basis of the invalidity of Generic Excluded Middle, a principle according to which any (...) sentence of the form ⌜Either Fs are G or Fs are not G⌝ is true. I argue that the kind-predication approach erroneously predicts that GEM is valid, and that it can only avoid this conclusion by either collapsing into a form of the quantificational analysis or otherwise garnering unpalatable metaphysical commitments. I also show that, while the quantificational approach does not validate GEM as a matter of logical form, the principle may be validated on certain semantic analyses of the generic operator, and so, such theories should be rejected. (shrink)

Generics and frequency statements are puzzling phenomena: they are lawlike, yet contingent. They may be true even in the absence of any supporting instances, and extending the size of their domain does not change their truth conditions. Generics and frequency statements are parametric on time, but not on possible worlds; they cannot be applied to temporary generalizations, and yet are contingent. These constructions require a regular distribution of events along the time axis. Truth judgments of generics vary considerably across speakers, (...) whereas truth judgments of frequency statements are much more uniform. A generic may be false even if the vast majority of individuals in its domain satisfy the predicated property, whereas a frequency statement using, e.g., usually would be true. This paper argues that all these seemingly unrelated puzzles have a single underlying cause: generics and frequency statements express probability judgments, and these, in turn, are interpreted as statements of hypothetical relative frequency. (shrink)

This book provides an up-to-date introduction to the study of generics and pursues the enterprise of the influential Generic Book edited by Gregory Carlson and Jeffry Pelletier, which was published in 1995. Genericity is a key notion in the study of human cognition as it reveals our capacity to organize our perceived reality into classes and to describe regularities. The generic can be expressed at the level of a word or phrase (ie the potato in The Irish economy (...) became dependent upon the potato) or an entire sentence (eg in John smokes a cigar after dinner, the generic aspect is a property of the expression, rather than any single word or phrase within it). This book gathers new work from senior and young researchers to reconsider the notion of genericity, examining the distinct contributions made by the determiner phrase (eg the notions of kind/individual) and the verbal predicate (eg the notions of permanency, disposition, ability, habituality, and plurality). Finally, in connection with the whole sentence, the analytic/synthetic distinction is discussed as well as the notion of normality. The book will appeal to both students and scholars in linguistics, philosophy and cognitive science. (shrink)

I contrast two approaches to the interpretation of generics such as ‘ravens are black:’ majority-based views, on which they are about what is the case most of the time, and inquiry-based views, on which they are about a feature we focus on in inquiry. I argue that majority-based views face far more systematic counterexamples than has previously been supposed. They cannot account for generics about kinds with multiple characteristic properties, such as ‘elephants live in Africa and Asia.’ I then go (...) on to sketch an inquiry-based view. (shrink)

Generic sentences (e.g., bare plural sentences such as “dogs have four legs” and “mosquitoes carry malaria”) are used to talk about kinds of things. Three experiments investigated the conceptual foundations of generics as well as claims within the formal semantic approaches to generics concerning the roles of prevalence, cue validity and normalcy in licensing generics. Two classes of generic sentences that pose challenges to both the conceptually based and formal semantic approaches to generics were investigated. Striking property (...) generics (e.g. “sharks bite swimmers”) are true even though only a tiny minority of instances have the property and thus pose obvious problems for quantificational approaches, and they also do not seem to characterize kinds in terms of the principled or statistical connections investigated in previous research ( Prasada and Dillingham, 2006 ; Prasada and Dillingham, 2009). The second class — minority characteristic generics (e.g. “ducks lay eggs”) — also poses serious problems for quantificational accounts, and appears to involve principled connections even though fewer than half of its instances have the relevant property. The experiments revealed three principal discoveries: first, striking generics involve neither principled nor statistical connections. Instead, they involve a causal connection between a kind and a property. Second, minority characteristic generics exhibit the characteristics of principled connections, which suggests that principled connections license the expectation that most instances will have the property, but do not require it. Finally, the experiments also provided evidence that prevalence and the acceptability of generics may be dissociated and provided data that are problematic for normalcy approaches to generics, and for the idea that cue validity licenses low prevalence generics. As such, the studies provided evidence in favor of a conceptually based approach to the semantics of generics ( Leslie, 2007 ; Leslie, 2008; see also Carlson, 2009). (shrink)

Generics about social kinds (or GSKs) frequently propagate descriptions that carry normative force (e.g., 'women are emotional'). Some philosophers of language attribute this to GSKs’ tendency to transmit essentialist beliefs about social kinds. According to these accounts, utterances of GSKs implicate that there is something in the nature of social kinds that causes them to possess the properties described, and that individual members of these social kinds therefore ought to exhibit (or be expected to exhibit) these properties. Here, I draw (...) on empirical evidence to suggest an alternative account. According to my framework, an utterance of a GSK implicates a distinction between the social kind described and its salient conceptual opposite, producing what I call a dichotomizing perspective. For example, ‘women are emotional’ suggests that men are not. Importantly, such distinctions frequently persist in the societal common ground as a function of social power, in part due to their alignment with hierarchical social structures between dichotomized social kinds. This enables such GSKs to perpetuate biased patterns of attention, expectation, and behavior even in the absence of essentialist belief. (shrink)

Scientists often communicate using generic generalizations, which are unquantified generalizations such as ‘Americans overestimate social class mobility’ or ‘sound waves carry gravitational mass’. In this paper, I explain the role of such generic generalizations in science, based on a novel theory about their characteristic meaning. According to this theory, a scientific generalization of the form ‘Ks are F’ says that F is one property based on which category K qualifies as a scientific kind. Because what it takes (...) to qualify as a scientific kind varies depending on the discipline, what a generic sentence entails also varies. Based on this semantic theory, I discuss the benefits and drawbacks of using generic language in science. (shrink)

The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown that the necessary and sufficient condition for there to be a negligible probability of the trajectory deviating significantly from the classical trajectory at any stage in the motion is that the state be a narrowly localised wave packet. The properties of the Bohmian trajectories are compared with those in the interpretation recently proposed by García de (...) Polavieja. The reasons why the latter tend to be much more nearly classical are discussed. The implications for other trajectory interpretations are considered. (shrink)

In this paper, we argue that, although neglected so far, there is a strong link between generics and testimonial injustice. Testimonial injustice is a form of epistemic injustice that “occurs when prejudice causes a hearer to give a deflated level of credibility to a speaker’s word”. Generics are sentences that express generalizations about a category or about its members without specifying what proportion of the category members possess the predicated property. We argue that generics are especially suited to cause (...) testimonial injustice for three reasons. First, generics elicit an “inferential asymmetry” :1452–1482, 2010). That is, generics are accepted even if only a few individuals possess the predicated property but are, nonetheless, taken to refer to almost all the members of the category. This peculiar combination makes generics particularly apt to cause testimonial injustice. High resistance to counter-evidence is a crucial feature of prejudice, the cause of testimonial injustice, and the more highly predictive a generalization the more it will be employed in concrete situations, leading to instances of testimonial injustice. Second, generics seem to play a key role in leading people to develop essentialist beliefs : 273–301, 2010; Rhodes et al. Proc Natl Acad Sci 109: 13526–13531, 2012). Subjects holding such beliefs treat categories as warranting strong generaliations over their members. Therefore, they will be more likely to rely on prejudice while dealing with the category members. Finally, generics are outstandingly common in everyday speech. Hence, their noxious effects are amplified by their diffusion and should not be underestimated. (shrink)

We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to existential closure, and another is defined via topological properties and Baire category theory. The second type of genericity was first formulated by Truss for automorphisms. We work with a later generalization, due to Ivanov, to finite tuples of predicates and functions. Let $N$ be a countable saturated model of some complete theory $T$ , and let $(N,\sigma)$ denote an expansion of (...) $N$ to the signature $L_{0}$ which is a model of some universal theory $T_{0}$ . We prove that when all existentially closed models of $T_{0}$ have the same existential theory, $(N,\sigma)$ is Truss generic if and only if $(N,\sigma)$ is an e-atomic model. When $T$ is $\omega$ -categorical and $T_{0}$ has a model companion $T_{\mathrm {mc}}$ , the e-atomic models are simply the atomic models of $T_{\mathrm {mc}}$. (shrink)

Generic statements, such as "Bees are striped" are thought to be a central vehicle by which essentialist beliefs are transmitted. But work on generics and essentialism almost never focuses on the type of properties mentioned in generic statements. We test the hypothesis that teleological properties, what something is for, affect categorization judgments more strongly than behavioral, biological, or social properties. In Experiment 1, participants categorized properties as being either behavioral, biological, social, or teleological. In Experiment 2, we used (...) the top four properties from each group to describe a generic noun or a specific individual. Participants then categorized creatures that had one of their properties transformed. We found that changes to teleological properties had the strongest impact on categorization judgments. In Experiment 3, we also found that teleological properties mattered more in an induction task. We suggest that teleological properties play this privileged role in categorization because they are treated as essential properties. (shrink)

A generic quantification, like dogs have tails, has a distinctive semantics; it is certainly not synonymous with the universal quantification all dogs have tails. A generic causal claim, like smoking causes cancer, is similarly not synonymous with all smoking causes cancer. Many philosophers of science have taken this difference in meaning to demand radical treatments of causal generics, invoking such exotica as causation between properties or causation at ‘different levels’. A more sober treatment is possible, making use of (...) a.. (shrink)

Christine Tappolet posed a problem for alethic pluralism: either deny the truth of conjunctions whose conjuncts are from distinct domains of inquiry, or posit a generic global truth property thus making other truth properties redundant. Douglas Edwards has attempted to solve the problem by avoiding the horns of Tappolet's dilemma. After first noting an unappreciated consequence of Edwards's view regarding a proliferation of truth properties, I show that Edwards's proposal fails to avoid Tappolet's original dilemma. His response is (...) not successful, as it lets in a generic truth property through the ‘back door’. I conclude by briefly offering a new solution to the problem, and an alternative diagnosis of Tappolet's dilemma.1. Tappolet's dilemmaThe alethic pluralist ; Sher ; Wright ) contends that propositions from different domains can be true in different ways. Mixed conjunctions have conjuncts from different domains; consider for example, ‘1+1=2 and murder is wrong’. A pressing question for the pluralist: if each conjunct is true in a distinct way, in what way is the conjunction true? Tappolet argues, " [M]ixed conjunctions need to be true in a further way. … But then each conjunct has to be true in the same way. This is what follows from the truism that a conjunction is true if and only if its conjuncts are true. Hence the question arises again why this further way of being true is not the only one we need. " Edwards puts Tappolet's contention as a dilemma: either admit a generic truth property that can apply to all propositions, regardless of domain or deny that mixed conjunctions can be true. It is prima facie plausible that mixed conjunctions can be true. Moreover, admitting a generic truth property would seemingly undermine alethic pluralism by making other truth properties redundant.2. Edwards's solutionEdwards's solution attempts …. (shrink)

In his book, "Prejudice", Endre Begby offers a novel and engaging account of the epistemology of prejudice which challenges some of the standard assumptions that have so far guided the recent discussion on the topic. One of Begby's central arguments against the standard view of prejudice, according to which a prejudiced person necessarily displays an epistemically culpable resistance to counterevidence, is that, qua stereotype judgments, prejudices can be flexible and rationally maintained upon encountering many disconfirming instances. By expanding on Begby's (...) analysis, I argue that, given the variety of truth conditions for true generic statements, the generic form of stereotype judgements can sometimes make prejudice extremely resistant to encounters with statistical facts about the distribution of the property among members of a certain group. At the same time, I argue that a more careful consideration of the generic form of stereotypes also allows us to recognize that evidence about how many members of the kind instantiate a property is not the only type of evidence which could disconfirm a prejudice. Evidence of no explanatory relation between a kind and a property should also have a direct effect on a prejudicial belief. For this reason, things may not look as dim for the standard view of prejudice in assessing paradigmatic instances of prejudicial beliefs as irrationally resistant to evidence. (shrink)

For a supersimple SU-rank 1 theory T we introduce the notion of a generic elementary pair of models of T . We show that the theory T* of all generic T-pairs is complete and supersimple. In the strongly minimal case, T* coincides with the theory of infinite dimensional pairs, which was used in 1184–1194) to study the geometric properties of T. In our SU-rank 1 setting, we use T* for the same purpose. In particular, we obtain a characterization (...) of linearity for SU-rank 1 structures by giving several equivalent conditions on T*, find a “weak” version of local modularity which is equivalent to linearity, show that linearity coincides with 1-basedness, and use the generic pairs to “recover” projective geometries over division rings from non-trivial linear SU-rank 1 structures. (shrink)

We study notions of genericity in models of, inspired by lines of inquiry initiated by Chatzidakis and Pillay and continued by Dolich, Miller and Steinhorn in general model‐theoretic contexts. These papers studied the theories obtained by adding a “random” predicate to a class of structures. Chatzidakis and Pillay axiomatized the theories obtained in this way. In this article, we look at the subsets of models of which satisfy the axiomatization given by Chatzidakis and Pillay; we refer to these subsets in (...) models of as CP‐generics. We study a more natural property, called strong CP‐genericity, which implies CP‐genericity. We use an arithmetic version of Cohen forcing to construct (strong) CP‐generics with various properties, including ones in which every element of the model is definable in the expansion, and, on the other extreme, ones in which the definable closure relation is unchanged. (shrink)

In the early nineties of the previous century, leaf languages were introduced as a means for the uniform characterization of many complexity classes, mainly in the range between P and PSPACE . It was shown that the separability of two complexity classes can be reduced to a combinatorial property of the corresponding defining leaf languages. In the present paper, it is shown that every separation obtained in this way holds for every generic oracle in the sense of Blum (...) and Impagliazzo. We obtain several consequences of this result, regarding, e. g., universal oracles, simultaneous separations and type-2 complexity. (shrink)

As a continuation of ideas initiated in [19], we study bi-colored (generic) expansions of geometric theories in the style of the Fraïssé–Hrushovski construction method. Here we examine that the properties $NTP_{2}$, strongness, $NSOP_{1}$, and simplicity can be transferred to the expansions. As a consequence, while the corresponding bi-colored expansion of a red non-principal ultraproduct of p-adic fields is $NTP_{2}$, the expansion of algebraically closed fields with generic automorphism is a simple theory. Furthermore, these theories are strong with $\operatorname (...) {\mathrm {bdn}}(\text {"}x=x\text {"})=(\aleph _0)_{-}$. (shrink)

A study of smooth classes whose generic structures have simple theory is carried out in a spirit similar to Hrushovski 147; Simplicity and the Lascar group, preprint, 1997) and Baldwin–Shi 1). We attach to a smooth class K0, of finite -structures a canonical inductive theory TNat, in an extension-by-definition of the language . Here TNat and the class of existentially closed models of =T+,EX, play an important role in description of the theory of the K0,-generic. We show that (...) if M is the K0,-generic then MEX. Furthermore, if this class is an elementary class then Th=Th). The investigations by Hrushovski and Pillay , provide a general theory for forking and simplicity for the nonelementary classes, and using these ideas, we show that if K0,, where {,*}, has the joint embedding property and is closed under the Independence Theorem Diagram then EX is simple. Moreover, we study cases where EX is an elementary class. We introduce the notion of semigenericity and show that if a K0,-semigeneric structure exists then EX is an elementary class and therefore the -theory of K0,-generic is near model complete. By this result we are able to give a new proof for a theorem of Baldwin and Shelah 1359). We conclude this paper by giving an example of a generic structure whose first-order theory is simple. (shrink)

I use generic embeddings induced by generic normal measures on that can be forced to exist if κ is an indestructibly weakly compact cardinal. These embeddings can be applied in order to obtain the forcing axioms in forcing extensions. This has consequences in : The Singular Cardinal Hypothesis holds above κ, and κ has a useful Jónsson-like property. This in turn implies that the countable tower works much like it does when κ is a Woodin limit of (...) Woodin cardinals. One consequence is that every set of reals in the Chang model is Lebesgue measurable and has the Baire Property, the Perfect Set Property and the Ramsey Property. So indestructible weak compactness has effects on cardinal arithmetic high up and also on the structure of sets of real numbers, down low, similar to supercompactness. (shrink)

We seem to talk about repeatable artworks, like symphonies, films, and novels, all the time. We say things like, "The Moonlight Sonata has three movements" and "Duck Soup makes me laugh". How are these sentences to be understood? We argue against the simple subject/predicate view, on which the subjects of the sentences refer to individuals and the sentences are true iff the referents of the subjects have the properties picked out by the predicates. We then consider two alternative responses that (...) involve reading these sentences as generics, similar to "The polar bear has four paws". The first response takes these sentences to be about kinds, and the second takes the relevant noun-phrases to act as predicates. We reject these accounts, but offer a third alternative which is informed by both, and which enables us to deny the existence of repeatable artworks while endorsing the truth of sentences seemingly about them. (shrink)

We present some general results concerning the topological space of cuts of a countable model of arithmetic given by a particular indicator Y.The notion of “indicator” is de.ned in a novel way, without initially specifying what property is indicated and is used to de.ne a topological space of cuts of the model. Various familiar properties of cuts are investigated in this sense, and several results are given stating whether or not the set of cuts having the property is (...) comeagre.A new notion of “generic cut” is introduced and investigated and it is shown in the case of countable arithmetically saturated models M ⊧ PA that generic cuts exist, indeed the set of generic cuts is comeagre in the sense of Baire, and furthermore that two generic cuts within the same “small interval” of the model are conjugate by an automorphism of the model.The paper concludes by outlining some applications to constructions of cuts satisfying properties incompatible with genericity, and discussing in model-theoretic terms those properties for which there is an indicator Y. (shrink)

Generic statements express generalizations about categories. Current theories suggest that people should be especially inclined to accept generics that involve threatening information. However, previous tests of this claim have focused on generics about non-human categories, which raises the question of whether this effect applies as readily to human categories. In Experiment 1, adults were more likely to accept generics involving a threatening property for artifacts, but this negativity bias did not also apply to human categories. Experiment 2 examined (...) an alternative hypothesis for this result, and Experiments 3 and 4 served as conceptual replications of the first experiment. Experiment 5 found that even preschoolers apply generics differently for humans and artifacts. Finally, Experiment 6 showed that these effects reflect differences between human and non-human categories more generally, as adults showed a negativity bias for categories of non-human animals, but not for categories of humans. These findings suggest the presence of important, early-emerging domain differences in people's judgments about generics. (shrink)

Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.

In this paper we introduce a generic large cardinal akin to, together with the consequences of being such a generic large cardinal. In this case is Jónsson, and in a choiceless inner model many properties hold that are in contrast with pcf theory in.

We use model theoretic forcing to study and generalize the construction of ()-generic models introduced by Kueker and Laskowski. We characterize the ()-generic models in terms of forcing and introduce a more general class of models, called essential forcing generics, which have many of the same properties.

LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a (...) class='Hi'>generic automorphism. In the present paper we give a weaker condition of this kind which is equivalent to the existence of generic automorphisms. Really we give more: a characterization of the existence of generic expansions (defined in an appropriate way) of an ω-categorical structure. We also show that Truss' condition guarantees the existence of a countable structure consisting of automorphisms ofMwhich can be considered as an atomic model of some theory naturally associated toM. We do it in a general context of weak models for second-order quantifiers.The author thanks Ludomir Newelski for pointing out a mistake in the first version of Theorem 1.2 and for interesting discussions. Also, the author is grateful to the referee for very helpful remarks. (shrink)

While finitely generic dimension groups are known to admit no proper self-embeddings, these groups also have no automorphisms other than scalar multiplications, and every countable infinitely generic dimension group admits proper self-embeddings and has automorphisms other than scalar multiplications. The finite-forcing companion of the theory of dimension groups is recursively isomorphic to first-order arithmetic, the infinite-forcing companion of the theory of dimension groups is recursively isomorphic to second-order arithmetic, and the first-order theory of existentially closed dimension groups is (...) a complete $\Pi_{1}^{1}$-set. While many special properties of f.g. dimension groups may be realized in recursive e.c. dimension groups, and many special properties of i.g. dimension groups may be realized in hyperarithmetic e.c. dimension groups, no f.g. dimension group is arithmetic and no i.g. dimension group is analytical. Yet there is an f.g. dimension group recursive in first-order arithmetic, and there is an i.g. dimension group recursive in second-order arithmetic. (shrink)