We show that the intersection of the class of 2-REA degrees with that of the ω-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.

We show that the Δ0 2 enumeration degrees are dense. We also show that for every nonzero n-c. e. e-degree a, with n≥ 3, one can always find a nonzero 3-c. e. e-degree b such that b < a on the other hand there is a nonzero ωc. e. e-degree which bounds no nonzero n-c. e. e-degree.

In this paper we study structural properties of n-c. e. Q-degrees. Two theorems contain results on the distribution of incomparable Q-degrees. In another theorem we prove that every incomplete Q-degree forms a minimal pair in the c. e. degrees with a Q-degree. In a further theorem it is proved that there exists a c. e. Q-degree that is not half of a minimal pair in the c. e. Q-degrees.

We prove that the degree structures of the d.c.e. and the 3-c.e. Turing degrees are not elementarily equivalent, thus refuting a conjecture of Downey. More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees f > e > d > 0 such that any degree u ≤ f is either comparable with both e and d, or incomparable with both.

We show that for any computably enumerable set A and any equation image set L, if L is low and equation image, then there is a c.e. splitting equation image such that equation image. In Particular, if L is low and n-c.e., then equation image is n-c.e. and hence there is no low maximal n-c.e. degree.

We provide three new results about interpolating 2-r.e. or 2-REA degrees between given r.e. degrees: Proposition 1.13. If c h are r.e. , c is low and h is high, then there is an a h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h g there is a properly d-r.e. degree a such that h a g and a is r.e. in h . Theorem 3.1. There is an incomplete nonrecursive r.e. A (...) such that every set REA in A and recursive in 0′ is of r. e. degree. The first proof is a variation on the construction of Soare and Stob . The second combines highness with a modified version of the proof strategy of Cooper et al. . The third theorem is a rather surprising result with a somewhat unusual proof strategy. Its proof is a 0‴ argument that at times moves left in the tree so that the accessible nodes are not linearly ordered at each stage. Thus the construction lacks a true path in the usual sense. Two substitute notions fill this role: The true nodes are the leftmost ones accessible infinitely often; the semitrue nodes are the leftmost ones such that there are infinitely many stages at which some extension is accessible. Another unusual feature of the construction is that it involves using distinct priority orderings to control the interactions of different parts of the construction. (shrink)

This volume contains papers from the recursion theory session of the Kazan Workshop on Recursion and Complexity Theory. Recursion theory, the study of computability, is an area of mathematical logic that has traditionally been particularly strong in the United States and the former Soviet Union. This was the first workshop ever to bring together about 50 international experts in recursion theory from the United States, the former Soviet Union and Western Europe.

We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees.

We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees.

We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle.

In this work, we study computable families of Turing degrees introduced and first studied by Arslanov and their numberings. We show that there exist finite families of Turing c.e. degrees both those with and without computable principal numberings and that every computable principal numbering of a family of Turing degrees is complete with respect to any element of the family. We also show that every computable family of Turing degrees has a complete with respect to each of its elements computable (...) numbering even if it has no principal numberings. It follows from results by Mal’tsev and Ershov that complete numberings have nice programming tools and computational properties such as Kleene’s recursion theorems, Rice’s theorem, Visser’s ADN theorem, etc. Thus, every computable family of Turing degrees has a computable numbering with these properties. Finally, we prove that the Rogers semilattice of each such non-empty non-singleton family is infinite and is not a lattice. (shrink)

The two volumes of letters by Mikhail Lifschitz, recently published in Russian, reveal for the first time certain aspects of his relationship with György Lukács and his general intellectual and cultural role in the long history of Soviet aesthetics. The first volume contains all the known letters between Lifschitz and Lukács; the second volume contains the letters from Lifschitz to three of his younger colleagues. Both volumes throw considerable light on the development of Marxist aesthetics in the Soviet Union from (...) the 1930s to the 1980s. The extensive commentaries and notes provide context for the various discussions in the letters and situate the main issues under consideration within the wider historical and social context of the period. (shrink)

In this paper, we prove several results about the Turing jumps of low c.e. sets. We show that only Δ‐levels of the Ershov Hierarchy can properly contain the Turing jumps of c.e. sets and that there exists an arbitrarily large computable ordinal with a normal notation such that the corresponding Δ‐level is proper for the Turing jump of some c.e. set. Next, we generalize the notion of jump traceability to the jump traceability with ‐ and ‐bound for every infinite computable (...) ordinal α. It is known that jump traceability and superlowness coincide on the c.e. sets and we show that for every infinite computable ordinal α, jump traceability with ‐ or ‐bound of a c.e. set A is equivalent to the fact that. Finally, we consider the generalized truth‐table reducibilities and prove that for every (not necessarily the Turing jump of a c.e. set) set A and every limit computable ordinal α, iff. (shrink)

A central premise of Ronald Dworkin’s famous Argument from Theoretical Disagreement is that judges regularly disagree about the grounds of law. The occurrence of these so-called ‘theoretical disagreements’, it is argued, cannot be explained by the influential legal positivist theory of HLA Hart according to which the grounds of law are constituted by judicial consensus. However, in his attempt to show that theoretical disagreements actually exist Dworkin primarily relies on the occurrence of judicial disagreements about legal interpretation, as he takes (...) them to be disagreements about the grounds of law. In this article, I will argue that these interpretive disagreements do not pose a problem for Hartian positivism. My argument will rely on standard work from the field of pragmatics which provides sophisticated explanations of how the interpretation of linguistic texts, such as legal documents, works. On the model that I will propose, interpretive disagreements concern the meaning that the legal authorities who enacted the document intended to get across and these disagreements arise from diverging assumptions about the context in which these documents were enacted. I will argue that disagreements about intentions and contextual presumptions do not concern the grounds of law and therefore do not threaten Hartian positivism. (shrink)

According to the Standard Picture of how law works, the content of the law that is created by legal texts such as statutes and constitutional provisions is determined by the meaning of these texts. Most proponents of this picture claim more specifically that the relevant notion of meaning in play is the communicative content of legal texts and that communicative content is itself determined by considerations of the intentions of legal authorities. In recent years, the Standard Picture has become the (...) subject of heated philosophical debate. Focusing on statutes as the paradigmatic type of legal texts, this thesis aims to contribute to this debate in two central ways. First, it argues that the aforementioned ‘intention-based’ versions of the Standard Picture lack convincing responses to three important objections that have been raised by critics. First, they lack an adequate account of how legislative bodies can be reasonably ascribed the intentions that they would need according to such versions. Second, they fail to explain important aspects of legal practice. Third, they provide at best a parochial theory of the content of the law that is generated by statutes. The second contribution is to provide a more sustained defence of the Standard Picture by developing a new ‘commitment-based’ version of this view. This version is based on an alternative theory of communication and claims that communicative content is not determined by considerations of intentions but rather by the commitments that are incurred by means of communicative acts. It is argued that this version can deal with the objections that have been raised by critics and therefore provides a more robust version of the Standard Picture. (shrink)

We consider so‐called extremal numberings that form the greatest or minimal degrees under the reducibility of all A‐computable numberings of a given family of subsets of, where A is an arbitrary oracle. Such numberings are very common in the literature and they are called universal and minimal A‐computable numberings, respectively. The main question of this paper is when a universal or a minimal A‐computable numbering satisfies the Recursion Theorem (with parameters). First we prove that the Turing degree of a set (...) A is hyperimmune if and only if every universal A‐computable numbering satisfies the Recursion Theorem. Next we prove that any universal A‐computable numbering satisfies the Recursion Theorem with parameters if A computes a non‐computable c.e. set. We also consider the property of precompleteness of universal numberings, which in turn is closely related to the Recursion Theorem. Ershov proved that a numbering is precomplete if and only if it satisfies the Recursion Theorem with parameters for partial computable functions. In this paper, we show that for a given A‐computable numbering, in the general case, the Recursion Theorem with parameters for total computable functions is not equivalent to the precompleteness of the numbering, even if it is universal. Finally we prove that if A is high, then any infinite A‐computable family has a minimal A‐computable numbering that satisfies the Recursion Theorem. (shrink)

A frequently discussed question in recent jurisprudential debates concerns the extent to which conversational implicatures can be conveyed reliably in legal language. Roughly, an implicature is a piece of information that a speaker communicates indirectly, that is without making the conveyed information explicit. According to the classical analysis of implicatures, their successful communication depends on a shared expectation of interlocutors to be cooperative in conversation. However, recently some legal theorists have claimed that in legal language implicatures tend to be unreliable (...) because – according to them – communicative cooperation cannot be presumed in legal discourse to the same extent as in ordinary conversations. In this article, I will focus on implicatures in a particular kind of legal discourse, namely judicial opinions, and I will discuss to what extent we should also be sceptical about implicatures in this type of legal discourse. My aim is to suggest that scepticism about the reliability of implicatures in judicial opinions appears implausible once we take evidence into account, i.e. examples of implicatures from judicial opinions. I will argue that the evidence that sceptics provide is not only scarce but inconclusive and present a wealth of implicatures from judicial opinions that are not unreliable. I will conclude that an evidence-based approach casts the sceptical view into doubt and suggest that communicative cooperation is presumed in judicial opinions, as well. (shrink)

The purpose of the study is to study the main criteria that ensure the development of the regional agricultural industry. Since the development of the subjects of Russia is based on the need to search for new management tools that ensure the long-term development of all sectors of the national economy, state support and state regulation play a special role in the management of the industry. The research focuses on two groups of industry development. The first group includes labor, natural, (...) material, technical and financial resources. The second group includes investment, information, innovation, research and production, and socio-infrastructural resources. However, the second group of resource base factors has a direct impact on the final position of the agricultural sector. As a result, a mechanism for managing the resources of the agricultural sector of the region, based on the growth factors of the agricultural sector, has been identified. (shrink)

It is proved that for every countable structure and a computable successor ordinal α there is a countable structure which is ‐least among all countable structures such that is Σ‐definable in the αth jump. We also show that this result does not hold for the limit ordinal. Moreover, we prove that there is no countable structure with the degree spectrum for.

We extend the limitwise monotonicity notion to the case of arbitrary computable linear ordering to get a set which is limitwise monotonic precisely in the non‐computable degrees. Also we get a series of connected non‐uniformity results to obtain new examples of non‐uniformly equivalent families of computable sets with the same enumeration degree spectrum.

The main question of this article is whether there is a family closed under finite differences (i.e., if A belongs to the family and B=∗A, then B also belongs to the family) that can be enumerated by any noncomputable c.e. degree, but which cannot be enumerated computably. This question was formulated by Greenberg et al. (2020) in their recent work in which families that are closed under finite differences, close to the Slaman–Wehner families, are deeply studied.

We introduce a hierarchy of sets which can be derived from the integers using countable collections. Such families can be coded into countable algebraic structures preserving their algorithmic properties. We prove that for different finite levels of the hierarchy the corresponding algebraic structures have different classes of possible degree spectra.

This collection addresses a post-WWII shift in the hierarchy of scientific explanations, where the highest goal moves from reductionism towards some ...

In much of the current academic and public discussion, conspiracy theories are portrayed as a negative phenomenon, linked to misinformation, mistrust in experts and institutions, and political propaganda. Rather surprisingly, however, philosophers working on this topic have been reluctant to incorporate a negatively evaluative aspect when either analyzing or engineering the concept conspiracy theory. In this paper, we present empirical data on the nature of the concept conspiracy theory from five studies designed to test the existence, prevalence and exact form (...) of an evaluative dimension to the ordinary concept conspiracy theory. These results reveal that, while there is a descriptive concept of conspiracy theory, the predominant use of conspiracy theory is deeply evaluative, encoding information about epistemic deficiency and often also derogatory and disparaging information. On the basis of these results, we present a new strategy for engineering conspiracy theory to promote theoretical investigations and institutional discussions of this phenomenon. We argue for engineering conspiracy theory to encode an epistemic evaluation, and to introduce a descriptive expression—such as ‘conspiratorial explanation’—to refer to the purely descriptive concept conspiracy theory. (shrink)

Contingency is the presence of non-actualized possibility in the world. Fatalism is a view of reality on which there is no contingency. Since it is contingency that permits agency, there has traditionally been much interest in contingency. This interest has long been embarrassed by the contention that simple and plausible assumptions about the world lead to fatalism. I begin with an Aristotelian argument as presented by Richard Taylor. Appreciation of this argument has been stultified by a question pertaining to the (...) source of necessity and possibility and a closely related one regarding the nature of metaphysics itself. Answering these questions reveals the crucial issue here, to wit, necessity and possibility in a temporal world. This issue is investigated through an important later criticism of Taylor by David Foster Wallace. Wallace’s critique is significant because it brings to the fore the pivotal notion for understanding contingency in a temporal world, that of synchronic possibility, the idea that incompatible states of affairs are possible at a single moment. This notion provides the basis of distinguishing two systematic accounts of truth, modality and time: two metaphysics of contingency. On one account, Taylor’s Aristotelian argument is straightforwardly valid and compelling; on the other, it is fallacious. In closing, I present reasons why the former account, supporting the Aristotelian views of time and truth, is correct and make some comments to ameliorate this conclusion. (shrink)