This article furnishes a systematisation of the Mediaval aesthetic vocabulary. This task is developed by means of the adoption of a dynamic of intersection among the various Aristotelic species qualitatis, which are taken as the basic structural elements of the requested system. Two versions of beauty are established, which will expand into two kinds of aesthetics, one leaded by pulchritudo, with intellectualistic implications and the other leaded by formositas, which will turn into an autonomus aesthetics; both of them have let (...) a strong legacy to contemporaneus aesthetics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:KARL ASCHENBRENNER, 19x 1-1988 Karl Aschenbrenner was born in Bison, Kansas, on November 20, 1911. He received the A. B. degree from Reed College in 1934 and his graduate degrees at Berkeley (M. A., 1938; Ph.D., 194o). After two years as an instructor at Reed College, he served in the U.S. Naval Reserve (Lieutenant in Meteorology ) from 1943 to 1946. From 1946 to 1948, he taught in the (...) Department of Speech at Berkeley and thereafter in the Department of Philosophy until his retirement in 1978. His teaching was devoted mainly to aesthetics and to the history of philosophy, most notably his course on Kant. For many years he was active as a trustee of the American Society for Aesthetics, and from 1961 as a member of the Journal's founding executive committee and, after incorporation, of the Board of Directors. Karl's first two years of attachment to theJournal coincided with service as chairman of the Department of Philosophy. This conjunction enabled him to be extraordinarily helpful in dealing with problems of bringing the Journal to birth--problems of funding, editorial appointments, publication policies, and business arrangements with the University of California Press. He welcomed the opportunity offered the Philosophy Department of collaborating in the publishing venture recommended by a special committee of the American Philosophical Association in 1958. The recognition early won by the Journal for its articles and reviews answered to his hope and work for success. At the annual meeting of the Board of Directors in San Francisco in 1987, the twenty-fifth birthday of the Journal was celebrated as was his twenty-seven years of diligent care for theJournafs excellence. Karl was a regular contributor to the philosophy series published by the University of California prior to three books issued by D. Reidel: The Concepts ofValue(1971), The ConceptsofCriticism(1974) and AnalysisofAppraisiveCharacterization (1983). He received Guggenheim, Fulbright, and NEH fellowships. Despite a physically disabling stroke in 1979, he continued his trips to Budapest which he began in 1972. He was concerned to study a non-IndoEuropean language spoken by people of European culture and had selected the Magyar tongue spoken in Hungary. He learned the language to test theories he advanced about appraisive concepts. He discovered in the structure of Magyar a mode of valuing embodied in verb usage differing significantly [333] 334 from the special appraisive vocabularies of English and German. Besides his lectures in Hungary, he responded to invitations to lecture received from universities in England, Austria, Poland, Bulgaria, and Romania. Shortly after his return to Budapest on his eleventh trip, he died of a massive stroke on July 4, 1988. He is buried there in a city he loved, especially for its music. He is survived by Marie, his wife of fifty-one years, and three children: Lisabeth, an attorney in Los Angeles; Peter, a judge in Fairbanks; and John, a composer in New York. E. W. STRONG... (shrink)

Assume that G is a definable group in a stable structure M. Newelski showed that the semigroup SG of complete types concentrated on G is an inverse limit of the ∞-definable semigroups SG,Δ. He also showed that it is strongly π-regular: for every p∈SG,Δ, there exists n∈N such that pn is in a subgroup of SG,Δ. We show that SG,Δ is in fact an intersection of definable semigroups, so SG is an inverse limit of definable semigroups, and that the latter (...) property is enjoyed by all ∞-definable semigroups in stable structures. (shrink)

We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable $\Pi _{1}^{0}$ subsets of 2ω and Kolmogorov complexity play a major role in the proof.

If κ is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which κ fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser.

Bayesians since Savage (1972) have appealed to asymptotic results to counter charges of excessive subjectivity. Their claim is that objectionable differences in prior probability judgments will vanish as agents learn from evidence, and individual agents will converge to the truth. Glymour (1980), Earman (1992) and others have voiced the complaint that the theorems used to support these claims tell us, not how probabilities updated on evidence will actually}behave in the limit, but merely how Bayesian agents believe they will behave, suggesting (...) that the theorems are too weak to underwrite notions of scientific objectivity and intersubjective agreement. I investigate, in a very general framework, the conditions under which updated probabilities actually converge to a settled opinion and the conditions under which the updated probabilities of two agents actually converge to the same settled opinion. I call this mode of convergence deterministic, and derive results that extend those found in Huttegger (2015b). The results here lead to a simple characterization of deterministic convergence for Bayesian learners and give rise to an interesting argument for what I call strong regularity, the view that probabilities of non-empty events should be bounded away from zero. (shrink)

An ω-set is a subset of the recursive ordinals whose complement with respect to the recursive ordinals is unbounded and has order type ω. This concept has proved fruitful in the study of sets in relation to metarecursion theory. We prove that the metadegrees of the sets coincide with those of the meta-r.e. ω-sets. We then show that, given any set, a metacomplete set can be found which is weakly metarecursive in it. It then follows that weak relative metarecursiveness is (...) not a transitive relation on the sets, extending a result of G. Driscoll [2, Theorem 3.1]. Coincidentally, we discuss the notions of total and complete regularity. Finally, we solve Post's problem for the transitive closure of weak relative metarecursiveness. We recommend the reader look at pp. 324–328 of the fundamental article [6] of Kreisel and Sacks before proceeding. He will find there a proof of the following very basic fact: a subset of the integers is iff it is metarecursively enumerable (metafinite). (shrink)

A set of integers A is computably encodable if every infinite set of integers has an infinite subset computing A. By a result of Solovay, the computably encodable sets are exactly the hyperarithmetic ones. In this article, we extend this notion of computable encodability to subsets of the Baire space, and we characterize the Π10-encodable compact sets as those which admit a nonempty Σ11-subset. Thanks to this equivalence, we prove that weak weak König’s lemma is not strongly computably reducible to (...) Ramsey’s theorem. This answers a question of Hirschfeldt and Jockusch. (shrink)

Say that α is an n-strongly c. e. real if α is a sum of n many strongly c. e. reals, and that α is regular if α is n-strongly c. e. for some n. Let Sn be the set of all n-strongly c. e. reals, Reg be the set of regular reals and CE be the set of c. e. reals. Then we have: S1 ⊂ S2 ⊂ · · · ⊂ Sn ⊂ · · · ⊂ ⊂ Reg (...) ⊂ CE. This gives a hierarchy of the c. e. reals. We also study the regularity of the d. c. e. reals. (shrink)

We study descriptive set theory in the space $^{\omega_1}\omega_1$ by letting trees with no uncountable branches play a similar role as countable ordinals in traditional descriptive set theory. By using such trees, we get, for example, a covering property for the class of $\Pi^1_1$-sets of $^{\omega_1}\omega_1$. We call a family $\mathscr{U}$ of trees universal for a class $\mathscr{V}$ of trees if $\mathscr{U} \subseteq \mathscr{V}$ and every tree in $\mathscr{V}$ can be order-preservingly mapped into a tree in $\mathscr{U}$. It is well (...) known that the class of countable trees with no infinite branches has a universal family of size $\aleph_1$. We shall study the smallest cardinality of a universal family for the class of trees of cardinality $\leq\aleph_1$ with no uncountable branches. We prove that this cardinality can be 1 (under $\neg$CH) and any regular cardinal $\kappa$ which satisfies $\aleph_2 \leq \kappa \leq 2^{\aleph_1}$ (under CH). This bears immediately on the covering property of the $\Pi^1_1$-subsets of the space $^{\omega_1}\omega_1$. We also study the possible cardinalities of definable subsets of $^{\omega_1}\omega_1$. We show that the statement that every definable subset of $^{\omega_1}\omega_1$ has cardinality $<\omega_n$ or cardinality $2^{\omega_1}$ is equiconsistent with ZFC (if $n \geq 3$) and with ZFC plus an inaccessible (if $n = 2$). Finally, we define an analogue of the notion of a Borel set for the space $^{\omega_1}\omega_1$ and prove a Souslin-Kleene type theorem for this notion. (shrink)

We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle $\square _{\lambda ,D}^{\mathit{fin}}$ introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ / D is not λ⁺⁺-universal and elementarily equivalent models M and N of size λ for which Mλ / D and Nλ / D are non-isomorphic. The question of the existence of such ultrafilters and models was (...) raised in [1]. (shrink)

We show a number of improvements in the use of Hidden Conditional Random Fields for phone classification on the TIMIT and Switchboard corpora. We first show that the use of regularization effectively prevents overfitting, improving over other methods such as early stopping. We then show that HCRFs are able to make use of non-independent features in phone classification, at least with small numbers of mixture components, while HMMs degrade due to their strong independence assumptions. Finally, we successfully apply Maximum (...) a Posteriori adaptation to HCRFs, decreasing the phone classification error rate in the Switchboard corpus by around 1% – 5% given only small amounts of adaptation data. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked (...) on many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

We define a hierarchy on the regular types of an ω-stable nonmultidimensional theory, using generalised notions of algebraic and strongly minimal formulae. As an application we show that any resplendent model of an ω-stable finite-dimensional theory is saturated.

This is a continuation of [3]. We deal with algebras of type : T ! N. Assume that V is a variety of type . Let p = x be a strongly nonregular identity satised in V , i.e. x; y are variables of p and x =6 y . For a variety K 2 L; E; R; S or RS denotes the set of all, regular, symmetric or regular and symmetric identities satised in K, respectively.

Neuropsychological dissociations between regular and irregular English past-tense morphology have been reported using a lexical decision task in which past-tense primes immediately precede present-tense targets. We present N400 event-related potential data from healthy participants using the same design. Both regular and irregular past-tense forms primed corresponding present-tense forms, but with a longer duration for irregular verbs. Phonological control conditions suggested that differences in formal overlap between prime and target contribute to, but do not account for, this difference, suggesting a link (...) between irregular morphology and semantics. Further analysis dividing the irregular verbs into two categories (weak irregular and strong) revealed that priming for strong verbs was reliably stronger than that for weak irregular and regular verbs, which were statistically indistinguishable from one another. We argue that, although we observe a regular-irregular dissociation, the nature of this dissociation is more consistent with single- than with dual-system models of inflectional morphology. (shrink)

If T is an unstable theory of cardinality <λ or countable stable theory with OTOP or countable superstable theory with DOP, λω λω1 in the superstable with DOP case) is regular and λ<λ=λ, then we construct for T strongly equivalent nonisomorphic models of cardinality λ. This can be viewed as a strong nonstructure theorem for such theories. We also consider the case when T is unsuperstable and develop further a result of Shelah about the existence of L∞,λ-equivalent nonisomorphic models (...) for such T. In addition, we show that a natural analogue of Scott's isomorphism theorem fails for models of power κ, if κω is regular, assuming κ<κ=κ. (shrink)

Assuming, we show that generalized eventually narrow sequences on a strongly inaccessible cardinal κ are preserved under a one step iteration of the Hechler forcing for adding a dominating κ‐real. Moreover, we show that if κ is strongly unfoldable, and λ is a regular cardinal such that, then there is a set generic extension in which.

This is an abstract of the paper to be submitted to Houston Journal of Mathematics. Our nomenclature and notation will be basically those of [3]. We shall consider algebras of type : T ! N, where T is a nonempty set, and N the set of all positive integers. By V we denote the set of all variables occurring in a polynomial symbol p. An identity p = q is called strongly non-regular if it is of the form p = (...) x for some binary polynomial symbol p, such that x; y 2 V and x =6 y. Let R denote the set of all regular identities of type . If K is a class of algebras of type , then E denotes the set of all identities satised by all algebras in K. We put R = E \ R. A variety K is called strongly non-regular if E contains some strongly non-regular identity. If is a set of identities of type , then K denotes the variety of algebras of type generated by ; E() will be the set of all identities which are consequences of . We put R() = E() \ R. We write ` e if there exists a nite proof of e starting from. (shrink)

This paper explores several topics related to Woodin’s HOD conjecture. We improve the large cardinal hypothesis of Woodin’s HOD dichotomy theorem from an extendible cardinal to a strongly compact cardinal. We show that assuming there is a strongly compact cardinal and the HOD hypothesis holds, there is no elementary embedding from HOD to HOD, settling a question of Woodin. We show that the HOD hypothesis is equivalent to a uniqueness property of elementary embeddings of levels of the cumulative hierarchy. We (...) prove that the HOD hypothesis holds if and only if every regular cardinal above the first strongly compact cardinal carries an ordinal definable [Formula: see text]-Jónsson algebra. We show that if the HOD hypothesis holds and HOD satisfies the Ultrapower Axiom, then every supercompact cardinal is supercompact in HOD. (shrink)

A cylindric algebra atom structure is said to be strongly representable if all atomic cylindric algebras with that atom structure are representable. This is equivalent to saying that the full complex algebra of the atom structure is a representable cylindric algebra. We show that for any finite n >3, the class of all strongly representable n-dimensional cylindric algebra atom structures is not closed under ultraproducts and is therefore not elementary. Our proof is based on the following construction. From an arbitrary (...) undirected, loop-free graph Γ, we construct an n-dimensional atom structure E(Γ), and prove, for infinite Γ, that E(Γ) is a strongly representable cylindric algebra atom structure if and only if the chromatic number of Γ is infinite. A construction of Erdős shows that there are graphs (k < ω)with infinite chromatic number, but having a non-principal ultraproduct $\prod _D\Gamma _k $ whose chromatic number is just two. It follows that $E(\Gamma _k )$ is strongly representable (each k < ω) but $\Pi _D E(\Gamma _k)$ is not. (shrink)

A question of Woodin asks if κ is strongly compact and GCH holds below κ, then must GCH hold everywhere? One variant of this question asks if κ is strongly compact and GCH fails at every regular cardinal δ < κ, then must GCH fail at some regular cardinal δ ≥ κ? Another variant asks if it is possible for GCH to fail at every limit cardinal less than or equal to a strongly compact cardinal κ. We get a negative (...) answer to the first of these questions and positive answers to the second of these questions for a supercompact cardinal κ in the context of the absence of the full Axiom of Choice. (shrink)

The main results in the paper are the following. Theorem A. Suppose that T is superstable and M ⊂ N are distinct models of T eq . Then there is a c ϵ N⧹M such that t is regular. For M ⊂ N two models we say that M ⊂ na N if for all a ϵ M and θ such that θ ≠ θ , there is a b ∈ θ ⧹ acl . Theorem B Suppose that T is (...) superstable , M ⊂ na N are models of T eq , and p is a regular type non-orthogonal to t . Then there is a c ϵ N such that t is regular and non-orthogonal to p. Furthermore, there is a formula θ ∈ t such that a ∈ θ and t ⊥ ̷ p ⇒ t is regular. We used these results to obtain ‘good’ tree decompositions of models in superstable theories with NDOP. See Definition 5.1 for the undefined terms. Theorem C Suppose that T is superstable with NDOP and M ⊨ T eq . Then every ⊂ na - decomposition inside M extends to a ⊂ na -decomposition of M. Furthermore, if 〈N η , a η : η ∈ I〉 is any ⊂ na -decomposition of M, then M is minimal over ∪N η and for all η ∈ I. M is dominated by ∪N η over N η . Using some stable group theory we show that when Th is superstable with NDOP and 〈 N η : η ∈ I 〉 is a tree decomposition of M, then M is constructible over ∪ n η with respect to a very strong isolation relation. (shrink)

Let k be an infinite cardinal. A subset of $(^k k)^n $ is a $\Sigma _1^1 $ -subset if it is the projection p[T] of all cofinal branches through a subtree T of $(lt;kk)^{n + 1} $ of height k. We define $\Sigma _k^1 - ,\Pi _k^1 $ - and $\Delta _k^1$ subsets of $(^k k)^n $ as usual. Given an uncountable regular cardinal k with k = k (...) there is a shrink)

We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters; among them: If m ≥ 1 and the ultrafilter D is , equation imagem)-regular, then D is κ -decomposable for some κ with λ ≤ κ ≤ 2λ ). If λ is a strong limit cardinal and D is , equation imagem)-regular, then either D is -regular or there are arbitrarily large κ < λ for which D is κ -decomposable ). Suppose that λ (...) is singular, λ < κ, cf κ ≠ cf λ and D is -regular. Then: D is either -regular, or -regular for some λ' < λ . If κ is regular, then D is either -regular, or -regular for every κ' < κ . If either λ is a strong limit cardinal and λ<λ < 2κ, or λ<λ < κ, then D is either λ -decomposable, or -regular for some λ' < λ . If λ is singular, D is -regular and there are arbitrarily large ν < λ for which D is ν -decomposable, then D is κ -decomposable for some κ with λ ≤ κ ≤ λ<μ . D × D' is -regular if and only if there is a ν such that D is -regular and D' is -regular for all ν∼ < ν .We also list some problems, and furnish applications to topological spaces and to extended logics. (shrink)

We study the first-order consequences of Ramsey’s Theorem fork-colourings ofn-tuples, for fixed$n, k \ge 2$, over the relatively weak second-order arithmetic theory$\mathrm {RCA}^*_0$. Using the Chong–Mourad coding lemma, we show that in a model of$\mathrm {RCA}^*_0$that does not satisfy$\Sigma ^0_1$induction,$\mathrm {RT}^n_k$is equivalent to its relativization to any proper$\Sigma ^0_1$-definable cut, so its truth value remains unchanged in all extensions of the model with the same first-order universe.We give a complete axiomatization of the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^n_k$for$n \ge (...) 3$. We show that they form a non-finitely axiomatizable subtheory of$\mathrm {PA}$whose$\Pi _3$fragment coincides with$\mathrm {B} \Sigma _1 + \exp $and whose$\Pi _{\ell +3}$fragment for$\ell \ge 1$lies between$\mathrm {I} \Sigma _\ell \Rightarrow \mathrm {B} \Sigma _{\ell +1}$and$\mathrm {B} \Sigma _{\ell +1}$. We also give a complete axiomatization of the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^2_k + \neg \mathrm {I} \Sigma _1$. In general, we show that the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^2_k$form a subtheory of$\mathrm {I} \Sigma _2$whose$\Pi _3$fragment coincides with$\mathrm {B} \Sigma _1 + \exp $and whose$\Pi _4$fragment is strictly weaker than$\mathrm {B} \Sigma _2$but not contained in$\mathrm {I} \Sigma _1$.Additionally, we consider a principle$\Delta ^0_2$-$\mathrm {RT}^2_2$which is defined like$\mathrm {RT}^2_2$but with both the$2$-colourings and the solutions allowed to be$\Delta ^0_2$-sets rather than just sets. We show that the behaviour of$\Delta ^0_2$-$\mathrm {RT}^2_2$over$\mathrm {RCA}_0 + \mathrm {B}\Sigma ^0_2$is in many ways analogous to that of$\mathrm {RT}^2_2$over$\mathrm {RCA}^*_0$, and that$\mathrm {RCA}_0 + \mathrm {B} \Sigma ^0_2 + \Delta ^0_2$-$\mathrm {RT}^2_2$is$\Pi _4$- but not$\Pi _5$-conservative over$\mathrm {B} \Sigma _2$. However, the statement we use to witness failure of$\Pi _5$-conservativity is not provable in$\mathrm {RCA}_0 +\mathrm {RT}^2_2$. (shrink)

Continuing the earlier research in [1] and [4] we work out a class of interstices in countable arithmetically saturated models of PA in which selective types are realized and a class of interstices in which 2-indiscernible types are realized.

Traditionally, Hume has widely been viewed as the standard-bearer for regularity accounts of causation. But between 1983 and 1990, two rival interpretations appeared—namely the skeptical realism of Wright, Craig, and Strawson, and the quasi-realist projectivism of Blackburn—and since then the interpretative debate has been dominated by the contest between these three approaches, with projectivism recently appearing the likely winner. This paper argues that the controversy largely arose from a fundamental mistake, namely, the assumption that Hume is committed to the (...) subjectivity of our conception of causal necessity. That assumption generated tensions within the regularity account, which the skeptical realist and quasi-realist alternatives, in very different ways, purported to resolve. But a broader and more balanced view of the textual evidence, taking due account of the relatively neglected sections where Hume applies the results of his analysis, tells strongly in favour of an objectivist regularity view, both in respect of causation and causal necessity. Despite some complications, the upshot is a far more straightforward reading of Hume than those that have hitherto dominated this long-running debate. (shrink)

The authors show. by means of a finitary version $\square_{\lambda D}^{fin}$ of the combinatorial principle $\square_\lambda^{h*}$ of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal A. if Mi and Ni are elementarily equivalent models of a language of size $\leq \lambda$ , then the second player has a winning strategy in the Ehrenfeucht- $Fra\uml{i}ss\acute{e}$ game of length $\lambda^{+}$ on $\pi_{i} M_{i}/D$ and $\pi_{i} N_{i}/D$ . (...) If in addition $2^{\lambda} = \labda^{+}$ and i < $\lambda$ implies | $M_{i}$ | +| $N_{i}$ | $\leq$ \lambda^{+} this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2]. (shrink)

In a recent paper by M. Rathjen and the present author it has been shown that the statement “every normal function has a derivative” is equivalent to $\Pi ^1_1$ -bar induction. The equivalence was proved over $\mathbf {ACA_0}$, for a suitable representation of normal functions in terms of dilators. In the present paper, we show that the statement “every normal function has at least one fixed point” is equivalent to $\Pi ^1_1$ -induction along the natural numbers.

Scanpaths have played an important role in classic research on reading behavior. Nevertheless, they have largely been neglected in later research perhaps due to a lack of suitable analytical tools. Recently, von der Malsburg and Vasishth proposed a new measure for quantifying differences between scanpaths and demonstrated that this measure can recover effects that were missed with the traditional eyetracking measures. However, the sentences used in that study were difficult to process and scanpath effects accordingly strong. The purpose of (...) the present study was to test the validity, sensitivity, and scope of applicability of the scanpath measure, using simple sentences that are typically read from left to right. We derived predictions for the regularity of scanpaths from the literature on oculomotor control, sentence processing, and cognitive aging and tested these predictions using the scanpath measure and a large database of eye movements. All predictions were confirmed: Sentences with short words and syntactically more difficult sentences elicited more irregular scanpaths. Also, older readers produced more irregular scanpaths than younger readers. In addition, we found an effect that was not reported earlier: Syntax had a smaller influence on the eye movements of older readers than on those of young readers. We discuss this interaction of syntactic parsing cost with age in terms of shifts in processing strategies and a decline of executive control as readers age. Overall, our results demonstrate the validity and sensitivity of the scanpath measure and thus establish it as a productive and versatile tool for reading research. (shrink)

We show that in the presence of the torsion tensor \, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by \. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, \, where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces the integration (...) in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: \^s}\rightarrow 4\pi U^{s-2}\sum _{l=1}^\infty \int _0^{\pi /2} d\phi \frac{\sin ^4\phi \,n^{s-3}}{[\sin \phi +U\varDelta n]^s}\), where \}\) and \ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: \. This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite. (shrink)

The present study investigated whether lexical access is affected by a regular phonological variation in connected speech: voice assimilation in French. Two associative priming experiments were conducted to determine whether strongly assimilated, potentially ambiguous word forms activate the conceptual representation of the underlying word. Would the ambiguous word form [sud] (either assimilated soute 'hold' or soude 'soda') facilitate 'bagage' 'luggage', which is semantically related to soute but not to soude? In Experiment 1, words in either canonical or strongly assimilated form (...) were presented as primes. Both forms primed their related target to the same extent. Potential lexical ambiguity did not modulate priming effects. In Experiment 2, the primes such as assimilated soute pronounced [sud] used in Experiment 1 were replaced with primes such as soude canonically pronounced [sud]. No semantic priming effect was obtained with these primes. Therefore, the effect observed for assimilated forms in Experiment 1 cannot be due to overall phonological proximity between canonical and assimilated forms. We propose that listeners must recover the intended words behind the assimilated forms through the exploitation of the remaining traces of the underlying form, however subtle these traces may be. (shrink)

In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both (...) with one (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values. (shrink)

Residence of unauthorized immigrants is a stable feature of the Global North’s liberal democracies. This article asks how liberal-democratic policymakers should respond to this phenomenon, assuming both that states have incontrovertible rights and interests to assert control over immigration and that unauthorized residence is nevertheless an entrenched fact. It argues that a set of liberal-democratic commitments gives policymakers strong reason to implement both so-called ‘firewall’ and ‘regularization’ policies, thereby protecting unauthorized immigrants’ basic needs and interests and officially incorporating many (...) of them in society. It then explains that the background imperative of immigration control creates a dilemmatic tension between these policies, as regularization is envisaged alongside the removal of the ineligible, which is in turn hindered by the implementation of firewalls. This creates a dilemma between the pursuit of two policy goals that are both underwritten by the same value commitments. Though it cannot be entirely dissolved, I argue that the best way to mitigate this dilemma is to design regularization policy in a way that leaves only a small number of unauthorized immigrants subject to removal. (shrink)

We show under that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is proper. This answers the question of Khomskii [7, Question 2.6.5]. We also show that the same conclusion holds under if we additionally assume that the set of Borel codes for I‐positive sets is. If we do not assume, the notion of properness becomes obscure as pointed out by Asperó and Karagila [1]. Using the notion of strong properness similar (...) to the one introduced by Bagaria and Bosch [2], we show under without using that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is strongly proper assuming every set of reals is ∞‐Borel and there is no ω1‐sequence of distinct reals. In particular, the same conclusion holds in a Solovay model. (shrink)

Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle’s state as it approaches the origin when the attractive coupling parameter is greater than the critical value of 1/4. Due to this unphysical divergence in oscillations, we are proposing that the interaction gets screened at short distances making the coupling parameter acquire an effective (renormalized) value that falls within the weak range 0–1/4. This prevents the oscillations (...) form growing without limit giving a lower bound to the energy spectrum and forcing the Hamiltonian of the system to be self-adjoint. Technically, this translates into a regularization scheme whereby the inverse square potential is replaced near the origin by another that has the same singularity but with a weak coupling strength. Here, we take the Eckart as the regularizing potential and obtain the corresponding solutions (discrete bound states and continuum scattering states). (shrink)

We introduce the Easton collapse and show that the two-stage iteration of Easton collapses gives a model in which the successor of a regular cardinal carries a strongly saturated filter. This allows one to get a model in which many successor cardinals carry saturated filters just by iterating Easton collapses.

König, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of a higher Souslin tree from the strong guessing principle.Complementary to the author’s work on the validity of diamond and non-saturation at the successor of singulars, we deal here with a successor of regulars. It is established that even the non-strong guessing principle entails non-saturation, and that, assuming the necessary cardinal arithmetic configuration, entails a diamond-type principle which suffices for the construction (...) of a higher Souslin tree.We also establish the consistency of GCH with the failure of the weakest form of generalized club guessing. This, in particular, settles a question from the original paper. (shrink)

For every uncountable regular cardinalκ and any cardinalλ≧κ,P κ λ denotes the set $\left\{ {x \subseteqq \lambda :\left| x \right|< \kappa } \right\}$ . Furthermore, < denotes the binary operation defined inP κ λ byx (...) + denotes the setP κ λ−I, andI * the filter dual toI.An idealI overP κ λ is said to benormal iff every functionf:P κ λ→λ with the property that {x∈P κ λ:f(x)∈x}∈I + is constant on a set inI +.I is said to bestrongly normal iff every functionf:P κ λ→P κ λ with the property that {x∈P κ λ:x∩xκ≠Ø∧f(x)shrink)

We give limits defined in terms of abstract pointclasses of the amount of determinacy available in certain canonical inner models involving strong cardinals. We show for example: Theorem A. $\mathrm{D}\mathrm{e}\mathrm{t}\text{\hspace{0.17em}}({\mathrm{\Pi }}_{1}^{1}-\mathrm{I}\mathrm{N}\mathrm{D})$ ⇒ there exists an inner model with a strong cardinal. Theorem B. Det(AQI) ⇒ there exist type-1 mice and hence inner models with proper classes of strong cardinals. where ${\mathrm{\Pi }}_{1}^{1}-\mathrm{I}\mathrm{N}\mathrm{D}\phantom{\rule{0ex}{0ex}}$ (AQI) is the pointclass of boldface ${\mathrm{\Pi }}_{1}^{1}$ -inductive (respectively arithmetically quasi-inductive) sets of reals.

It has been suggested that damage to anterior regions of the left hemisphere results in a dissociation in the perception and lexical activation of past-tense forms. Specifically, in a lexical-decision task in which past-tense primes immediately precede present-tense targets, such patients demonstrate significant priming for irregular verbs (spoke–speak), but, unlike control participants, fail to do so for regular verbs (looked–look). Here, this behavioral dissociation was first confirmed in a group of eleven patients with damage to the pars opercularis (BA 44) (...) and pars triangularis (BA 45) of the left inferior frontal gyrus (i.e., Broca's area). Two conditions containing word-onset orthographic–phonological overlap (bead–bee, barge–bar) demonstrated that the disrupted regular-verb priming was accompanied by, and covaried with, disrupted ortho-phonological priming, regardless of whether prime stimuli contained the regular inflectional rhyme pattern. Further, the dissociation between impaired regular-verb and preserved irregular-verb priming was shown to be continuous rather than categorical; priming for weak-irregular verbs (spent–spend) was intermediate in size between that of regular verbs and strong verbs. Such continuous dissociations grounded in ortho-phonological relationships between present- and past-tense forms are predicted by single-system, connectionist approaches to inflectional morphology and not predicted by current dual-system, rule-based models. Event-related potential data demonstrated that N400 priming effects were intact for both regular and irregular verbs, suggesting that the absence of significant regular-verb priming in the response time data did not result from a disruption of lexical access, and may have stemmed instead from post-lexical events such as covert articulation, segmentation strategies, and/or cognitive control. (shrink)

The strong continuity principle reads “every pointwise continuous function from a complete separable metric space to a metric space is uniformly continuous near each compact image.” We show that this principle is equivalent to the fan theorem for monotone \ bars. We work in the context of constructive reverse mathematics.

This study uses panel data to investigate the different roles of the Chinese government in influencing companies’ decision making about corporate environmental reporting (CER) via a two-stage process. The results show that the Chinese government appears to mainly influence the decision whether to disclose or not, but has limited influence on how much firms disclose. The results also show that the traditional model of authoritarian capitalism (under which state-owned enterprises [SOEs] are the major governance arrangement) is transforming into a new (...) model. In the new model of authoritarian capitalism, the Chinese government uses newer, more sophisticated tools to manage both state-owned and non–state-owned companies. In addition, these new governance arrangements appear to be more efficient than the traditional model. The findings of this study have implications for both the Chinese government and for Chinese companies, as well as making important contributions to the literature and knowledge of CER in China. (shrink)

We force and construct models in which there are non-supercompact strongly compact cardinals which aren't measurable limits of strongly compact cardinals and in which level by level equivalence between strong compactness and supercompactness holds non-trivially except at strongly compact cardinals. In these models, every measurable cardinal κ which isn't either strongly compact or a witness to a certain phenomenon first discovered by Menas is such that for every regular cardinal λ > κ, κ is λ strongly compact iff κ (...) is λ supercompact. (shrink)