By a result of L.D. Beklemishev, the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over any $$\Pi _2$$ -axiomatizable base theory extending Elementary Arithmetic collapses to its first level. We prove that this result cannot in general be extended to base theories of arbitrary quantifier complexity. In fact, given any recursively enumerable set of true $$\Pi _2$$ -sentences, S, we construct a sound $$(\Sigma _2 \! \vee \! \Pi _2)$$ -axiomatized theory T extending S such that the (...) hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over T is proper. Our construction uses some results on subrecursive degree theory obtained by L. Kristiansen. (shrink)

For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained restricting the schemes of induction, minimization and (a version of) collection to Δ n+1 (T) formulas. We obtain conditions on T (T is an extension of B * Δ n+1 (T) or Δ n+1 (T) is closed (in T) under bounded quantification) under which IΔ n+1 (T) and LΔ n+1 (T) are equivalent. These conditions depend (...) on Th Πn +2 (T), the Π n+2 –consequences of T. The first condition is connected with descriptions of Th Πn +2 (T) as IΣ n plus a class of nondecreasing total Π n –functions, and the second one is related with the equivalence between Δ n+1 (T)–formulas and bounded formulas (of a language extending the language of Arithmetic). This last property is closely tied to a general version of a well known theorem of R. Parikh. Using what we call Π n –envelopes we give uniform descriptions of the previous classes of nondecreasing total Π n –functions. Π n –envelopes are a generalization of envelopes (see [10]) and are closely related to indicators (see [12]). Finally, we study the hierarchy of theories IΔ n+1 (IΣ m ), m≥n, and prove a hierarchy theorem. (shrink)

We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.

We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.

LetTbe a recursive theory in the language of first order Arithmetic. We prove that ifTextends: (a) the scheme of parameter free Δ1-minimization (plusexp). or (b) the scheme of parameter free Π1-induction, then there are no Σ1-maximal models with respect toT. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect toIΔ0+expdo not satisfy the scheme of Σ1-collectionBΣ1.

We characterize the sets of all Π2 and all equation image theorems of IΠ−1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ−n + 1 is conservative over IΣ−n with respect to equation image sentences cannot be extended to Πn + 2 sentences. © 2011 WILEY-VCH Verlag (...) GmbH & Co. KGaA, Weinheim. (shrink)

We prove that the standard cut is definable in each existentially closed model ofIΔ0+ exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic.

By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only consistent Πn+1-theory which extends the scheme of induction for parameter free Πn+1-formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first-order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain (...) results on the quantifier complexity, finite axiomatizability and relative strength of schemes for Δn+1-formulas. (shrink)

This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are $${\Delta_1}$$ provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether $${I\Delta_0 + \neg \mathit{exp}}$$ implies $${B\Sigma_1}$$ to a purely recursion-theoretic question.

In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that IΔ n+1 (T) is Π n+2 –axiomatizable. In particular, IΔ n+1 (IΔ n+1 ) gives an axiomatization of Th Π n+2 (IΔ n+1 ) and is not finitely axiomatizable. This fact relates the fragment IΔ n+1 (IΔ n+1 ) to induction (...) rule for Δ n+1 –formulas. Our arguments, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons’ conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for Π n+2 and Δ n+1 formulas (see [2]). (shrink)

A well known theorem proved by J. Paris and H. Friedman states that BΣn +1 is a Πn +2-conservative extension of IΣn . In this paper, as a continuation of our previous work on collection schemes for Δn +1-formulas , we study a general version of this theorem and characterize theories T such that T + BΣn +1 is a Πn +2-conservative extension of T . We prove that this conservativeness property is equivalent to a model-theoretic property relating Πn-envelopes and (...) Πn-indicators for T . The analysis of Σn +1-collection we develop here is also applied to Σn +1-induction using Parsons' conservativeness theorem instead of Friedman-Paris' theorem.As a corollary, our work provides new model-theoretic proofs of two theorems of R. Kaye, J. Paris and C. Dimitracopoulos : BΣn +1 and IΣn +1 are Σn +3-conservative extensions of their parameter free versions, BΣ–n +1 and IΣ–n +1. (shrink)

The state of computing science and, particularly, software engineering and knowledge engineering is generally considered immature. The best starting point for achieving a mature engineering discipline is a solid scientific theory, and the primary reason behind the immaturity in these fields is precisely that computing science still has no such agreed upon underlying theory. As theories in other fields of science do, this paper formally establishes the fundamental elements and postulates making up a first attempt at a theory in this (...) field, considering the features and peculiarities of computing science. The fundamental elements of this approach are informons and holons, and it is a general and comprehensive theory of software engineering and knowledge engineering that related disciplines (e.g., information systems) can particularise and/or extend to take benefit from it (Lakatos’ concepts of core theory and protective belt theories). (shrink)

Known as the Darwin of the twenty-first century, the German biologist Ernst Walter Mayr (1904-2005) studied a great variety of subjects such as Ornithology, Genetics, Evolution, Classification, History, and Philosophy of Biology. This scientist was a giant of the previous century and an icon of Evolutionary Biology. He became famous for his Biological Species Concept and his conclusion that allopatry is the main cause for the origin of species. He provided a decisive contribution to the New Systematics and was the (...) pioneer of the punctuated equilibrium idea. Mayr was one of the main architects of the evolutionary synthesis as also of the Neo-Darwinian wave. Evaluated together, all of his works reveal several elements of his ambition – to organize a philosophical conception inherent for Biology. An assiduous defender of autonomous Biology, Mayr asserted that four sets of factors in Biology differ from those in the Exact Sciences: (I) refutation of essentialism, mechanism, vitalism, and teleology; (II) some physical principles cannot be applied to Biology; (III) absence of general laws in Biology; and (IV) basic principles of biology and their specific character cannot be applied to the inanimate world. The present study took as an axis a minor or even invisible theme from the Ernst Mayr literature and aims to analyze critically the theoretical and epistemological basis that subsidizes – or not– the affirmation that Biology is an autonomous Science. - O biólogo alemão Ernst Walter Mayr (1904-2005), conhecido como o Darwin do século XXI, trabalhou com uma grande variedade de temas: Ornitologia, Genética, Evolução, Classificação, História e Filosofia da Biologia. Esse cientista foi um dos gigantes do século XX e um ícone para a Biologia Evolutiva. Ficou famoso com o seu Conceito Biológico de Espécie e sua conclusão de que a alopatria era a principal causa da origem das espécies. Forneceu uma contribuição decisiva à Nova Sistemática, foi precursor da ideia de equilíbrio pontuado e um dos principais arquitetos da síntese evolutiva, bem como do movimento Neodarwinista. Quando avaliados em conjunto, seus trabalhos revelam os diversos elementos de sua ambição – organizar um corpo de concepções filosóficas próprias da Biologia. Defensor assíduo de uma Biologia autônoma, Mayr afirmou que há quatro conjuntos de fatores que diferenciam a Biologia do conjunto das Ciências Exatas: (I) refutação do essencialismo, do mecanicismo, do vitalismo e da teleologia; (II) convicção de que certos princípios da Física não podem ser aplicados à Biologia; (III) ausência de leis naturais universais em Biologia; e (IV) percepção do caráter único de certos princípios básicos da Biologia não aplicáveis ao mundo inanimado. O presente artigo tomou por eixo um tema aparentemente menor ou mesmo invisível na obra de Ernst Mayr e pretende realizar uma análise crítica acerca de suas bases teóricas e epistemológicas que subsidiaram – ou não – a afirmação da Biologia como uma Ciência autônoma. (shrink)

Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall \,\lambda (...) < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred–O–RFN{0=1}.Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, ${\rm{RCA}}_0^{\rm{*}}$ be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,$${\rm{ATR}}_0 \equiv {\rm{RCA}}_0^{\rm{*}} + {\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - RFN}}\,_{{\bf{\Pi }}_2^1 } \left.$$We may even replace ${\rm{RCA}}_0^{\rm{*}}$ by the weaker ECA0, the second-order analogue of Elementary Arithmetic.Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles. (shrink)

This article uses a well-defined setting to suggest an optimistic view about the distributional effects of immigration. Section 2 provides a general picture of the native-immigrant differences in labour force participation, unemployment, and occupational and educational attainment, taking skill levels and years since immigration into account. Section 3 investigates the inequality impact of immigration by summarizing the potential labour market impacts and the wage and employment consequences. Section 4 deals with the potentially slow integration of immigrants into the labour market (...) of the host country, as well as with the role that self-selection and selection through politically set admission rules can play for the performance in the labour market. It also considers cultural or ethnic identity as an independent factor potentially affecting economic success and discusses the consequences for inequality. Section 5 concludes. (shrink)

This work aims to rescue, transcribe and create new artistic and cultural expressions through the use of native peoples’ historical visual recordings, integrating intelligent technologies. For this purpose, a Chilean native peoples’ digital repository is collected, in order to apply a Digital Humanities-based methodology. From the chosen material, portraits are selected, recoloured through a AI-based model; the facial mesh is constructed using a facial landmark detector; the points of the mesh are reconstructed by a Delaunay triangulation; to finally apply an (...) additive manufacturing process. Thus, these physical pieces allow to compare the native people’s own physiognomies, creating new cultural expressions. (shrink)

Disjunctivism about perceptual appearances, as I conceive of it, is a theory which seeks to preserve a na.

Emotion evaluations are assumed to play a crucial role in the emotion regulation process. We tested a postulate from our framework of emotion dysregulation (Nowak, U., Wittkamp, M. F., Clamor, A., & Lincoln, T. M. [2021]. Using the Ball-in-Bowl metaphor to outline an integrative framework for understanding dysregulated emotion. Frontiers in Psychiatry, 12, 118), namely that the extent to which individuals evaluate an emotion as harmful and their personal resources to modify and accept/tolerate the emotion as sufficient predict the subsequent (...) use of regulation strategies. Participants (n = 118) from a community sample took part in an experience-sampling assessment over 7 days including 10 daily paired measurements. The first measured momentary affective valence and arousal along with harmfulness evaluations and evaluations of personal resources to modify and accept/tolerate an emotion. The second followed three minutes later and measured emotion regulation strategies. The more harmful individuals evaluated an emotion, the more likely they were to use an emotion regulation strategy. The more harmful individuals evaluated an emotion, and the less sufficient they evaluated their personal resources to accept/tolerate an emotion, the more likely they were to use a maladaptive emotion regulation strategy. We conclude that emotions that people evaluate as harmful or difficult to accept are most likely to be regulated in a maladaptive manner. This implies that modifying beliefs about emotions could represent a promising treatment approach. (shrink)

A common finding is that information order influences belief revision (e.g., Hogarth & Einhorn, 1992). We tested personal experience as a possible mitigator. In three experiments participants experienced the probabilistic relationship between pieces of information and object category through a series of trials where they assigned objects (planes) into one of two possible categories (hostile or commercial), given two sequentially presented pieces of probabilistic information (route and ID), and then they had to indicate their belief about the object category before (...) feedback. The results generally confirm the predictions from the Hogarth and Einhorn model. Participants showed a recency effect in their belief revision. Extending previous model evaluations the results indicate that the model predictions also hold for classification decisions, and for pieces of information that vary in their diagnostic values. Personal experience does not appear to prevent order effects in classification decisions based on sequentially presented pieces of information and in belief revision. (shrink)