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)

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)

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

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)

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)

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)

For the theorists of crisis, the revolutionary state comes into existence through violence, and due to its inability to provide an authoritative katechon (restrainer) against internal and external violence, it perpetuates violence until it self-destructs. Writing during extreme economic depression and growing social and political violence, the crisis theorists––Joseph de Maistre, Juan Donoso Cortés, and Carl Schmitt––each sought to blame the chaos of their time upon the Janus-faced postrevolutionary ideals of liberalism and socialism by urging a return to pre-revolutionary moral (...) and religious values. They are united by three counterrevolutionary principles, all of which are purported to remedy revolutionary violence: traditional constitutional fidelity, the philosophy of the decision, and opposition to bourgeois liberalism. This essay is followed by the first complete English translation and publication of Donoso’s letter of October 24, 1851, which contains Donoso’s only reference to the “discussing class,” a political entity later popularized by Schmitt in his 1922 work Political Theology. (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.

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)

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.

Some theories of goodness are descriptively rich: they have much to say about what makes things good. Neo-Aristotelian accounts, for instance, detail the various features that make a human being, a dog, a bee good relative to facts about those forms of life. Famously, such theories of relative goodness tend to be comparatively poor: they have little or nothing to say about what makes one kind of being better than another kind. Other theories of goodness—those that take there to be (...) absolute goodness—are comparatively rich: they offer grounds for judging some types of things better than others because they have more absolute goodness. Moorean accounts, for example, can tell us that humans and human experiences are superior to bees and blades of grass. But such theories tend to be descriptively poor: they struggle to tell us in virtue of what this is so. In this essay we motivate and flesh out a view that splits the difference between accounts of goodness as relative and accounts of goodness as absolute. Such a view holds promise only if the mechanics of this kind of metaphysics of goodness can be worked out. Here we present a view on which the paradigm for absolute goodness is God and the paradigm for each kind of relative goodness is a divine idea. (shrink)

Since 1900, debates about the justification of punishment have also been debates about the cause of crime. In the early twentieth century, the rehabilitative ideal of punishment viewed mental illness and dysfunction in individuals as the cause of crime. Starting in the 1970s, retributivism identified the immorality of human agents as the source of crime, which dovetailed well with the “tough-on-crime” political milieu of the 1980s and 1990s that produced mass incarceration. After surveying these historical trends, Wirts argues for a (...) social critical view that crime is best understood as a product of an unjust society, not faulty human beings. This view should take the lessons learned by the critiques of rehabilitation, however, and resist the tendency to reduce human beings to recipients of social services. (shrink)

Donald Davidson has made enormous contributions to the philosophy of action, epistemology, semantics and philosophy of mind and today is recognized as one of the most important analytical philosophers of the late twentieth century. _Donald Davidson: Truth, Meaning and Knowledge_ addresses * Davidson's writings on epistemology and theory of language with their implications of ontology and philosophy of mind * the central issue of whether truth is the ultimate goal of enquiry, challenged by contributions from Richard Rorty and Paul Horwich (...) * Davidson's approach to semantics and applied linguistics as addressed by Kirk Ludwig, Gabriel Segal, Peter Pagin, Stephen Neale, Herman Cappelen and Ernie Lepore and Reinaldo Elugardo * Davidson's advances in the philosophy of mind in relation to the views of Williard V. Quine, John McDowell and Peter F. Strawson, in essays by Roger Gibson and Anita Avramides. (shrink)