In the first half of the 1970s, two books appeared which have subsequently been regarded as major works in political philosophy: John Rawls's A Theory of Justice, and Robert Nozick's Anarchy, State, and Utopia. Economists have devoted a considerable amount of ink to commentary, pro and con, on A Theory of Justice; and it is getting to be a rare public finance textbook that does not, in its discussion of governmental redistribution, describe the Kantian contract made behind the veil of (...) ignorance. On the other hand, while Nozick has not exactly been ignored, economists have not joined the debate over Anarchy, State, and Utopia with the same gusto. When economists have joined the debate, their concern has been, more often than not, with Nozick's entitlement theory of distributive justice, as is the case with Varian and Sen. What is largely missing, then, is any economic analysis of the processes that give rise to Nozick's morally legitimate state, which he calls the minimal state, and the characteristics and likely activities of the minimal state within the moral boundaries set by Nozick, his assertions to the contrary notwithstanding. (shrink)

This article examines how minimal genome research mobilizes philosophical concepts such as minimality and essentiality. Following a historical approach the article aims to uncover what function this terminology plays and which problems are raised by them. Specifically, four historical moments are examined, linked to the work of Harold J. Morowitz, Mitsuhiro Itaya, Eugene Koonin and Arcady Mushegian, and J. Craig Venter. What this survey shows is a historical shift away from historical questions about life or descriptive questions about specific (...) organisms towards questions that explore biological possibilities: what are possible forms of minimal genomes, regardless of whether they exist in nature? Moreover, it highlights a fundamental ambiguity at work in minimal genome research between a universality claim and a standardization claim: does a minimal genome refer to the minimal gene set for any organism whatsoever? Or does it refer rather to a gene set that will provide stable, robust and predictable behaviour, suited for biotechnological applications? Two diagnoses are proposed for this ambiguity: a philosophical diagnosis of how minimal genome research either misunderstands the ontology of biological entities or philosophically misarticulates scientific practice. Secondly, a historical diagnosis that suggests that this ambiguity is part of a broader shift towards technoscience. (shrink)

The political systems of the Roman Republic were based almost entirely on tradition, “the way of the ancestors”, rather than on a written constitution. While the founders of the American Republic looked to ancient Rome as a primary model for their enterprise, nevertheless, in line with the rationalist spirit of their age, the American founders attempted to create a rational set of rules that would guide the conduct of American politics, namely, the US Constitution.These two examples offer a striking case (...) of the ideal types, famously delineated by Michael Oakeshott in “Rationalism in Politics” and elsewhere, between politics as a practice grounded in tradition and politics as a system based on principles flowing from abstract reasoning.This book explores how the histories of the two republics can help us to understand Oakeshott’s claims about rational versus traditional politics. Through examining such issues we may come to understand better not only Oakeshott’s critique of rationalism, but also modern constitutional theory, issues in the design of the European Union, and aspects of the revival of republicanism. (shrink)

ABSTRACT Nassim Taleb’s dismissal of history as based on the “narrative fallacy”—which reads our present knowledge of past events into our reconstruction of the past—is based on a fundamental misconception of what historians actually do. Historians do not, as Taleb presumes, try to infer general, predictive laws from “hard” facts, as do natural scientists; instead their aim is to discover the causes of unique historical facts among antecedent facts. This is no different, in principle, from “narrating” the cause of a (...) supernova by referring to physical causes. The construction of universal historical laws would admittedly be a fool’s errand, but that is not the task historians—as opposed to historicists—actually set for themselves. (shrink)

ABSTRACT Nassim Taleb’s dismissal of history as based on the “narrative fallacy”—which reads our present knowledge of past events into our reconstruction of the past—is based on a fundamental misconception of what historians actually do. Historians do not, as Taleb presumes, try to infer general, predictive laws from “hard” facts, as do natural scientists; instead their aim is to discover the causes of unique historical facts among antecedent facts. This is no different, in principle, from “narrating” the cause of a (...) supernova by referring to physical causes. The construction of universal historical laws would admittedly be a fool’s errand, but that is not the task historians—as opposed to historicists—actually set for themselves. (shrink)

The article presents three models of radical cultural practice: Adorno’s dissonant modernism, Brecht’s “functional transformation” or “re-functioning” of institutions through estrangement and dialectical realism, and Debord’s Situationist détournement of art, aiming to rupture and decolonize naturalized everyday life. The three models all begin with a critical appropriation of the traditions of art and aims at resisting the social power that passes through art, as an institutionalized field of production and activity. Each of the three modes establishes a set of productive (...) strategies. (shrink)

In a very literarily complicated setting, Frater Taciturnus sets a remark about Hamlet not being a Christian tragedy. After unpeeling that literary setting and noting that Taciturnus' remark aims more at Jacob Börne than at Shakespeare, the paper shows how Frater Taciturnus' remark calls into question the religious project of a certain danish author. For, Taciturnus' primary concern is to show that religious drama is not possible, or at least "ought not be." This general law applies to Hamlet as well, (...) and if Shakespeare was attempting a religious drama he a) shouldn't have because such a thing is essentially undramatizable, and b) failed because he did not begin (which would be possible) by showing the hero's religious presuppositions. Frater Taciturnus himself has given considerable thought to the extent and the manner in which the religious can be represented; in fact the letter to the reader is his proof of how perfectly his own narrative, "Guilty/Not Guilty," was constructed with precisely these problems in mind. The play is not the thing that Taciturnus is really interested in, nor is he interested in the playwright's intentions, he considers that the play's the thing that catches out Börne's misunderstanding of the religious, and it is this field—in particular, that area where the religious life and literary art intersect, that is the brother's interest and forte. But if Taciturnus is correct in his criticism of Börne, it should be impossible for S. Kierkegaard to produce a religious authorship as well. (shrink)

We all live our daily lives surrounded by the products of technology that make what we do simpler, faster, and more efficient. These are benefits we often just take for granted. But at the same time, as these products disburden us of unwanted tasks that consumed much time and effort in earlier eras, many of them also leave us more disengaged from our natural and even human surroundings. It is the task of what Gene Moriarty calls focal engineering to (...) create products that will achieve a balance between disburdenment and engagement: “How much disburdenment will be appropriate while still permitting an engagement that enriches one’s life, elevates the spirit, and calls forth a good life in a convivial society?” One of his examples of a focally engineered structure is the Golden Gate Bridge, which “draws people to it, enlivens and elevates the human spirit, and resonates with the world of its congenial setting. Humans, bridge, and world are in tune.” These values of engagement, enlivenment, and resonance are key to the normative approach Moriarty brings to the profession of engineering, which traditionally has focused mainly on technical measures of evaluation such as efficiency, productivity, objectivity, and precision. These measures, while important, look at the engineered product in a local and limited sense. But “from a broader perspective, what is locally benign may present serious moral problems,” undermining “social justice, environmental sustainability, and health and safety of affected parties.” It is this broader perspective that is championed by focal engineering, the subject of Part III of the book, which Moriarty contrasts with “modern” engineering in Part I and “pre-modern” engineering in Part II. (shrink)

This paper reads through some contemporary literary critical problems and theorizing about textuality to Augustine's Confessions, to the enrichment, if not the ecstasy of both contemporary and medieval thinking. It shows that Augustine is both aware of much that passes as new in theorizing about language, and that his text is argumentatively and rhetorically structured to set difference at play. Like Augustine's writing, this article is a performance piece: besides arguing, it acknowledges; beside demonstration, it questions; besides telling, it shows; (...) it would not be called a study of textuality in Augustine, but a performance of textuality with (in) Augustine. (shrink)

Prefaced by an argument that the ancients understood mimesis as fundamental to being human, and art as therefore essential to human moral and intellectual development, this book starts from the problematic status of the (happily ending) Iphigenia in Poetics. How Aristotle must explicate tragedy to hold Iphigenia as the best thus sets up the exploration of comedy. Chapter two shows that comedy aims at the catharsis of desire and sympathy. This analysis is then applied in detail to Aristophanes’ Acharnians, Shakespeare’s (...) As You Like It and Stoppard’s Arcadia, exhibiting the cross-cultural application of the theory which Aristotle would expect. (shrink)

Kant's famous statement (from the first Critique) that he found it necessary to deny knowledge in order to make room for faith acknowledges a religious or theological telos to the entire critical project. This article outlines a series of relations of 'knowledge' to 'faith' in the architectonic repetitions with variation that plays from the first Critique through the Religion. Various deployments of 'truth' at each stage presume a kind of 'faith' or trust all the way along. These deployments are shown (...) to follow a pattern which echoes that set out in Northrop Frye's understanding of literary modes descending from myth to romance to high and low mimetic and ending in the ironic. These modes describe realms of possibility and necessity, and their nesting in Frye's explication of literature is shown to be itself an echo of more formal theories of Tarski and Godel. (shrink)

Why would an empiricist look at a poem? And if he did, what could he find? This paper begins with Hume's programmatic statement for literary renewal based on the empirical principles set forth in the first Enquiry, and raises the question about the worth of poetry according to those principles. There is little "abstract reasoning concerning quantity or number, or experimental reasoning concerning matter of fact and existence" in poetry and so "commit it to the flames." The second Enquiry allows (...) that since disputation among men is based on the passions, poetry might have a place as a means to speak to the affections, to inforce particular sophistries close to our hearts. The second half of the paper defends poetry on grounds opposed to the premises of empirical science. Specifically, whereas in science knowledge is power, in the arts knowledge is suffering, or,where science aims at mastery and ownership, poetry relates us to that in being which is not ours. This view is explicated by use of King Lear. (shrink)

How should the “physical” in “physicalism” be understood? I here set out systematic criteria of adequacy, propose an account, and show how the account meets those criteria. The criteria of adequacy focus on the idea of rational management: to vindicate philosophical practice, the account must make it plausible that we can assess various questions about physicalism. The account on offer is dubbed the “Ideal Naturalist Physics” account, according to which the physical is that which appears in an ideal theory that (...) both meets the explanatory goals of physics and is naturalist in a sense to be explained. The combination of these two provides a satisfying account of the physical that meets the criteria of adequacy and can be used to predict puzzle cases as well. (shrink)

In his Consciousness and Fundamental Reality (2017) Philip Goff defends his anti-physicalist argument against what he calls the "Dual Carving" objection—the idea that two representations of the very same fact could both be conceptually independent and "transparent," that is, revealing of the essences of the entities in question. His defense invokes a thesis he calls "Minimal Rationalism." I explore exactly how Minimal Rationalism is supposed to turn aside the objection and argue that the formulation of Minimal Rationalism (...) on offer is ambiguous between stronger and weaker readings. Goff needs the stronger reading to use it in defense of his argument, but only the weaker reading is warranted by the considerations he brings to bear in favor of his rationalism. His minimal rationalism is, in sum, insufficiently minimal. The upshot is not only that Goff is deprived of a way of turning back an important objection to his case against physicalism; we also gain a better sense of what kind of rationalist thesis is properly invoked in metaphysics. (shrink)

What has come to be known as “a priori physicalism” is the thesis, roughly, that the non-physical truths in the actual world can be deduced a priori from a complete physical description of the actual world. To many contemporary philosophers, a priori physicalism seems extremely implausible. In this paper I distinguish two kinds of a priori physicalism. One sort – strict a priori physicalism – I reject as both unmotivated and implausible. The other sort – liberal a priori physicalism – (...) I argue is both motivated and plausible. This variety of a priori physicalism insists that the necessitation of non-physical truths by the physical facts must be underwritten in a certain fashion by a priori knowledge, but the a priori knowledge need not amount to a simple deduction of the non-physical truths from a complete physical description of the world. Further, this sort of liberal a priori physicalism has the advantage that it offers hope for a genuinely satisfying account of how the physical facts manage to necessitate the facts about phenomenal consciousness – thereby in effect solving the “hard problem” of consciousness. The first half of the paper sets out the motivation for liberal a priori physicalism and its superiority to the strict version; the second half presents one strategy available to the liberal a priori physicalist for showing how consciousness can be accommodated in a purely physical world. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Mimesis: Culture, Art, SocietyGene FendtMimesis: Culture, Art, Society, by Gunter Gebauer and Christoph Wulf; translated by Don Reneau; 400 pp. Berkeley: University of California Press, 1995, $45.00 cloth, $18.00 paper.The purpose of this book is to develop “a historical reconstruction of important phases in the development of mimesis” (p. 1) from a brief discussion of its pre-Platonic Greek significance through contemporary thinkers. It is, then, not strictly a (...) philosophical text, as are most of the texts and authors the book takes up. It is, however, a significant effort in the history of ideas, and as such it is shot through with traces of the traditional tropes, shaping power, ideology, and even social relations of that discipline, particularly as it is practiced in the venerable school of German scholarship. That is, the structure, tone, and argument of the book are shaped mimetically. This book’s problematic is, then, not simply historical, as Republic’s problem with the poets is not simply philosophical. Rather, both books partake of mimesis, even while each one aims to criticize or set forth the concept’s historical development.Let this stand as notice of a deep philosophical problem with the method of historical criticism. In fairness we should note that the authors are not unconscious of their difficulty here: “The fact that mimesis cannot be represented without the use of mimetic processes poses the fundamental problem of theory formation in reference to our object. What is the relation between the representational and the represented world? Is the representation of representation structurally equivalent to simple representation?” (p. 21). The authors hope to moot the power of those questions, if not the questions themselves, by attending “first of all to representations of mimesis found in texts best selected for that purpose and only afterward begin to offer considerations of a more generalizing nature” (p. 21). Their reasoning and choice of texts here is the traditional trope of the discipline: a mimema. Among other things, this methodos requires that the authors treat Girard as developing a “literary critical examination of [mimesis in] nineteenth and twentieth century novels” (p. 359n1) and a “new ordering of nineteenth century social relations” (p. 235), rather than, as he claims, a comprehensive anthropological thesis. At least, this method requires treating the former as essential, and the latter as less justifiable, for if Girard’s anthropological thesis about mimesis were justifiable a history of the idea of mimesis would be merely a heresiology. This problem can be restated mutatis mutandis for such thinkers as Plato and Augustine, whose theses—if they have theses—about mimesis are deeply anthropological.Two further questions arise early on and remain at the end. If, as the authors hold (and show), “the concept of mimesis necessarily loses its intellectual centrality with the rise of rational thought,” so much so that “the field of art, which comes to be regarded in the process as autonomous, undergoes a complete and fundamental restructuring” (p. 3), must we not begin to [End Page 199] suspect—as recent philosophers like Derrida attempt to show—that there is a dialectical relationship between the intentional, truth-functional relations of modern rational thought and the mimetic, unformalizable and “ambivalent” (pp. 2–3) processes of mimesis? Rather than conclude that “the question what is mimesis? is one which demonstratively leads to error” (p. 309), does it not begin to seem that intentional representation, as most visible in science, and mimetic assimilations, as most obviously effective in art, are together the necessary dialectical elements of culture, art and science? While it seems that the rise of rational scientific thought pushes mimesis to the social fringes of the arts, isn’t scientific activity and writing still just as much subject, and just as much a product, of the power of mimesis as art? Similarly art is just as bound as science to “probability” or “the convincing impossibility,” to recall Aristotle. This idea is not entirely foreign to the book; it appears subliminally as a plausible explication of the work of theorists like Benjamin and Adorno (pp. 267–93).The third difficulty is a question about selection. As in Auerbach’s renowned precursor, Wulf... (shrink)

Assembly of minimal genomes revealed many genes encoding unknown functions. Three overlooked functional categories account for some of them. Cells are prone to make errors and age. As a first key function, discrimination between proper and changed entities is indispensable. Discrimination requires management of information, an authentic, yet abstract, cur- rency of reality. For example proteins age, sometimes very fast. The cell must identify, then get rid of old proteins without destroying young ones. Implementing discrimination in cells leads to (...) the second set of functions, usually ignored. Being abstract, information must nevertheless be embodied into material entities, with unavoidable idiosyncratic properties. This brings about novel unmet needs. Hence, the buildup of cells elicits specific but awkward material implementations, ‘kludges’ that become essential under particular settings, while difficult to identify. Finally, a third functional category char- acterizes the need for growth, with metabolic implementations allowing the cell to put together the growth of its cytoplasm, membranes, and genome, spanning different spatial dimensions. Solving this metabolic quandary, critical for engineering novel synthetic biology chassis, uncovered an unexpected role for CTP synthetase as the coordinator of nonhomothetic growth. Because a significant number of SynBio constructs aim at creating cell factories we expect that they will be attacked by viruses (it is not by chance that the function of the CRISPR system was identified in industrial settings). Substantiating the role of CTP, natural selection has dealt with this hurdle via synthesis of the antimetabolite 30-deoxy-30,40-didehydro- CTP, recruited for antiviral immunity in all domains of life. (shrink)

Theoretical minimal RNA rings attempt to mimick life’s primitive RNAs. At most 25 22-nucleotide-long RNA rings code once for each biotic amino acid, a start and a stop codon and form a stem-loop hairpin, resembling consensus tRNAs. We calculated, for each RNA ring’s 22 potential splicing positions, similarities of predicted secondary structures with tRNA vs. rRNA secondary structures. Assuming rRNAs partly derived from tRNA accretions, we predict positive associations between relative secondary structure similarities with rRNAs over tRNAs and genetic (...) code integration orders of RNA ring anticodon cognate amino acids. Analyses consider for each secondary structure all nucleotide triplets as potential anticodon. Anticodons for ancient, chemically inert cognate amino acids are most frequent in the 25 RNA rings. For RNA rings with primordial cognate amino acids according to tRNA-homology-derived anticodons, tRNA-homology and coding sequences coincide, these are separate for predicted cognate amino acids that presumably integrated late the genetic code. RNA ring secondary structure similarity with rRNA over tRNA secondary structures associates best with genetic code integration orders of anticodon cognate amino acids when assuming split anticodons (one and two nucleotides at the spliced RNA ring 5′ and 3′ extremities, respectively), and at predicted anticodon location in the spliced RNA ring’s midst. Results confirm RNA ring homologies with tRNAs and CDs, ancestral status of tRNA half genes split at anticodons, the tRNA-rRNA axis of RNA evolution, and that single theoretical minimal RNA rings potentially produce near-complete proto-tRNA sets. Hence genetic code pre-existence determines 25 short circular gene- and tRNA-like RNAs. Accounting for each potential splicing position, each RNA ring potentially translates most amino acids, realistically mimicks evolution of the tRNA-rRNA translation machinery. These RNA rings ‘of creation’ remind the uroboros’ (snake biting its tail) symbolism for creative regeneration. (shrink)

Prokaryotic genomes of endosymbionts and parasites are examples of naturally evolved minimal cells, the study of which can shed light on life in its minimum form. Their diverse biology, their lack of a large set of orthologous genes and the existence of essential linage (and environmentally) specific genes all illustrate the diversity of genes building up naturally evolved minimal cells. This conclusion is reinforced by the fact that sometimes the same essential function is performed by genes from different (...) evolutionary origins. Nevertheless, all cells perform a set of life‐essential functions however different their cell machinery and environment in which they thrive. An upcoming challenge for biologists will be to discern, by studying differences and similarities in current biodiversity, how cells with reduced genomes have adapted while retaining all basic life‐supporting functions. (shrink)

Synthetic genomics is a new field of research in which small DNA pieces are assembled in a series of steps into whole genomes. The highly reduced genomes of host‐associated bacteria are now being used as models for de novo synthesis of small genomes in the laboratory. Bacteria with the smallest genomes identified in nature provide nutrients to their hosts, such as amino acids, co‐factors and vitamins. Comparative genomics of these bacteria enables predictions to be made about the gene sets (...) required for core cellular functions and the associated metabolic network for the biosynthesis of host‐selected compounds. Synthetic biology may ultimately enable researchers to make customized cell‐specific organelles for the production and delivery of drugs to humans and domestic animals. Synthetic genomics may also become the method of choice for functional analyses of genes and genomes from bacteria that cannot be cultivated in the laboratory. (shrink)

Against the opinion that DNA as program is not sufficiently explanatory, we maintain that the cellular machinery is entirely computational, and we identify the crucial notion of the interpreter that expresses the gene with the minimal gene set. Epigenetics research does not so much need paradigm shifts as the unraveling of an exceedingly complex computational machine.

We study generalizations of shortest programs as they pertain to Schaefer’s problem. We identify sets of -minimal and -minimal indices and characterize their truth-table and Turing degrees. In particular, we show , , and that there exists a Kolmogorov numbering ψ satisfying both and . This Kolmogorov numbering also achieves maximal truth-table degree for other sets of minimal indices. Finally, we show that the set of shortest descriptions, , is 2-c.e. but not co-2-c.e. Some open problems are (...) left for the reader. (shrink)

One of the fundamental ethical concerns about biomedical research is that it frequently exposes participants to risks for the benefit of others. To protect participants’ rights and interests in this context, research regulations and guidelines set out a mix of substantive and procedural requirements for research involving humans. Risk thresholds play an important role in formulating both types of requirements. First, risk thresholds serve to set upper risk limits in certain types of research. Second, risk thresholds serve to demarcate risk (...) categories that streamline risk-adapted systems of ethical oversight. But although risk thresholds play such an important role in research governance, there is a need both to better define the existing risk thresholds and to delineate new thresholds in order to develop more risk-adapted systems of research oversight. The present paper examines the existing minimal risk threshold and the surrounding debates with the goal of deriving a systematic approach to setting thresholds of research risk. (shrink)

The development of synthetic biology calls for accurate understanding of the critical functions that allow construction and operation of a living cell. Besides coding for ubiquitous structures, minimal genomes encode a wealth of functions that dissipate energy in an unanticipated way. Analysis of these functions shows that they are meant to manage information under conditions when discrimination of substrates in a noisy background is preferred over a simple recognition process. We show here that many of these functions, including transporters (...) and the ribosome construction machinery, behave as would behave a material implementation of the informationmanaging agent theorized by Maxwell almost 150 years ago and commonly known as Maxwell’s demon (MxD). A core gene set encoding these functions belongs to the minimal genome required to allow the construction of an autonomous cell. These MxDs allow the cell to perform computations in an energy-efficient way that is vastly better than our contemporary computers. (shrink)

An oracle A is low-for-speed if it is unable to speed up the computation of a set which is already computable: if a decidable language can be decided in time $t(n)$ using A as an oracle, then it can be decided without an oracle in time $p(t(n))$ for some polynomial p. The existence of a set which is low-for-speed was first shown by Bayer and Slaman who constructed a non-computable computably enumerable set which is low-for-speed. In this paper we answer (...) a question previously raised by Bienvenu and Downey, who asked whether there is a minimal degree which is low-for-speed. The standard method of constructing a set of minimal degree via forcing is incompatible with making the set low-for-speed; but we are able to use an interesting new combination of forcing and full approximation to construct a set which is both of minimal degree and low-for-speed. (shrink)

We prove a cell decomposition theorem for Presburger sets and introduce a dimension theory for Z-groups with the Presburger structure. Using the cell decomposition theorem we obtain a full classification of Presburger sets up to definable bijection. We also exhibit a tight connection between the definable sets in an arbitrary p-minimal field and Presburger sets in its value group. We give a negative result about expansions of Presburger structures and prove uniform elimination of imaginaries for Presburger structures within the (...) Presburger language. (shrink)

Minimal Semantics asks what a theory of literal linguistic meaning is for - if you were to be given a working theory of meaning for a language right now, what would you be able to do with it? Emma Borg sets out to defend a formal approach to semantic theorising from a relatively new type of opponent - advocates of what she call 'dual pragmatics'. According to dual pragmatists, rich pragmatic processes play two distinct roles in linguistic comprehension: as (...) well as operating in a post-semantic capacity to determine the implicatures of an utterance, they also operate prior to the determination of truth-conditional content for a sentence. That is to say, they have an integral role to play within what is usually thought of as the semantic realm. Borg believes dual pragmatic accounts constitute the strongest contemporary challenge to standard formal approaches to semantics since they challenge the formal theorist to show not merely that there is some role for formal processes on route to determination of semantic content, but that such processes are sufficient for determining content. Minimal Semantics provides a detailed examination of this school of thought, introducing readers who are unfamiliar with the topic to key ideas like relevance theory and contextualism, and looking in detail at where these accounts diverge from the formal approach. Borg's defence of formal semantics has two main parts: first, she argues that the formal approach is most naturally compatible with an important and well-grounded psychological theory, namely the Fodorian modular picture of the mind. Then she argues that the main arguments adduced by dual pragmatists against formal semantics - concerning apparent contextual intrusions into semantic content - can in fact be countered by a formal theory. The defence holds, however, only if we are sensitive to the proper conditions of success for a semantic theory. Specifically, we should reject a range of onerous constraints on semantic theorizing (e.g., that it answer epistemic or metaphysical questions, or that it explain our communicative skills) and instead adopt a quite minimal picture of semantics. (shrink)

Let (M, ≤,...) denote a Boolean ordered o-minimal structure. We prove that a Boolean subalgebra of M determined by an algebraically closed subset contains no dense atoms. We show that Boolean algebras with finitely many atoms do not admit proper expansions with o-minimal theory. The proof involves decomposition of any definable set into finitely many pairwise disjoint cells, i.e., definable sets of an especially simple nature. This leads to the conclusion that Boolean ordered structures with o-minimal theories (...) are essentially bidefinable with Boolean algebras with finitely many atoms, expanded by naming constants. We also discuss the problem of existence of proper o-minimal expansions of Boolean algebras. (shrink)

We prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures.

Let D be a strongly minimal set in the language L, and $D' \supset D$ an elementary extension with infinite dimension over D. Add to L a unary predicate symbol D and let T' be the theory of the structure (D', D), where D interprets the predicate D. It is known that T' is ω-stable. We prove Theorem A. If D is not locally modular, then T' has Morley rank ω. We say that a strongly minimal set D (...) is pseudoprojective if it is nontrivial and there is a $k < \omega$ such that, for all a, b ∈ D and closed $X \subset D, a \in \mathrm{cl}(Xb) \Rightarrow$ there is a $Y \subset X$ with a ∈ cl(Yb) and |Y| ≤ k. Using Theorem A, we prove Theorem B. If a strongly minimal set D is pseudoprojective, then D is locally projective. The following result of Hrushovski's (proved in $\S4$ ) plays a part in the proof of Theorem B. Theorem C. Suppose that D is strongly minimal, and there is some proper elementary extension D1 of D such that the theory of the pair (D1, D) is ω1-categorical. Then D is locally modular. (shrink)

We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytically separate sets in , and we can definably analytically approximate definable continuous unary functions. A similar statement holds for definable smooth functions.

We extend Meyer's 1972 investigation of sets of minimal indices. Blum showed that minimal index sets are immune, and we show that they are also immune against high levels of the arithmetic hierarchy. We give optimal immunity results for sets of minimal indices with respect to the arithmetic hierarchy, and we illustrate with an intuitive example that immunity is not simply a refinement of arithmetic complexity. Of particular note here are the fact that there are three (...) class='Hi'>minimal index sets located in Π3 − Σ3 with distinct levels of immunity and that certain immunity properties depend on the choice of underlying acceptable numbering. We show that minimal index sets are never hyperimmune; however, they can be immune against the arithmetic sets. Lastly, we investigate Turing degrees for sets of random strings defined with respect to Bagchi's size-function s. (shrink)

This paper began as a generalization of a part of the author's PhD thesis about ACFA and ended up with a characterization of groups definable in T A . The thesis concerns minimal formulae of the form x ∈ A ∧ σ(x) = f(x) for an algebraic curve A and a dominant rational function f: A → σ(A). These are shown to be uniform in the Zilber trichotomy, and the pairs (A, f) that fall into each of the three (...) cases are characterized. These characterizations are definable in families. This paper covers approximately half of the thesis, namely those parts of it which can be made purely model-theoretic by moving from ACFA, the model companion of the class of algebraically closed fields with an endomorphism, to T A , the model companion of the class of models of an arbitrary totally-transcendental theory T with an injective endomorphism, if this model-companion exists. A T A analog of the characterization of groups definable in ACFA is obtained in the process. The full characterization of the cases of the Zilber trichotomy in the thesis is obtained from these intermediate results with heavy use of algebraic geometry. (shrink)

TheoremEvery model of ZFChas a conservative elementary extension which possesses a cofinal minimal elementary extension.An application of Boolean ultrapowers to models of full arithmetic is also presented.

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the (...) SEU preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted. (shrink)

We construct a strongly minimal set which is not a finite cover of one with DMP. We also show that for a strongly minimal theory T, generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and Pillay.

It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known. In (...) this note we construct, in ZFC, ${2^{\mathfrak{c}}}$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces. (shrink)

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [2] for sets and functions definable in models of weakly o-minimal theories. We pay special (...) attention to large subsets of Cartesian products of definable sets, showing that if X, Y and S are non-empty definable sets and S is a large subset of X × Y, then for a large set of tuples $\langle \overline{a}_{1},\ldots,\overline{a}_{2^{k}}\rangle \in X^{2^{k}}$ , where k = dim(Y), the union of fibers $S_{\overline{a}_{1}}\cup \cdots \cup S_{\overline{a}_{2^{k}}}$ is large in Y. Finally, given a weakly o-minimal structure ������, we find various conditions equivalent to the fact that the topological dimension in ������ enjoys the addition property. (shrink)