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.

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 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)

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 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)

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (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)

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)

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.

This paper is an update of the documents we have concerning the Acts of the Christian martyrs, focused on three main aspects: 1) the kind of acts we know of and their classification from the point of view of their historic value; 2) the versions or editions of the texts that are most accepted by scholars; 3) the relevance of the different parts that make up these documents in order to discern the original text from passages that were rewritten or (...) underwent later variations. In this way, the article offers an exhaustive list of the documents for use in researching Christian martyrs in the Roman 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)

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.

In recent literature, panpsychism has been defended by appeal to two main arguments: first, an argument from philosophy of mind, according to which panpsychism is the only view which successfully integrates consciousness into the physical world (Strawson 2006; Chalmers 2013); second, an argument from categorical properties, according to which panpsychism offers the only positive account of the categorical or intrinsic nature of physical reality (Seager 2006; Adams 2007; Alter and Nagasawa 2012). Historically, however, panpsychism has also been defended by appeal (...) to a third argument based on considerations about the nature and observability of causation. This argument has not been much discussed in recent times. Here is a concise version from William James: "… the concrete perceptual flux, taken just as it comes, offers in our own activity-situations perfectly comprehensible instances of causal agency … If we took these experiences as the type of what actual causation is, we should have to ascribe to cases of causation outside of our life, to physical cases also, an inwardly experiential nature. In other words, we should have to espouse a so-called “pan-psychic” philosophy" (James 1911: 218). James here suggests that we have direct experience of causation in our own agency. He thereby directly contradicts David Hume, who famously denied that we have any experience of causation. James goes on to claim that if this experience is representative of causation in general, it follows that all causation is mental, and that panpsychism is true. This kind of argument for panpsychism can be called the argument from (experience of) causation. This chapter offers, first, a history of this argument and arguments closely related to it, and second, an analysis of the argument – is it valid, are its premises in any way defensible, and how does it relate to the other, more popular arguments for panpsychism from philosophy of mind and categorical properties? (shrink)

Ibn al-ʻArabī, 1165-1240; views on freedom; Sufism; Islamic philosophy.

Greek text, english translation and commentary on the surviving fragments of Empedocles (fragments as known in 1981, does not include more recent finds).

Contrary to Vaesen's argument that humans are unique with respect to nine cognitive capacities essential for tool use, we suggest that although such cognitive processes contribute to variation in tool use, it does not follow that these capacities arenecessaryfor tool use, nor that tool use shaped cognition per se, given the available data in cognitive neuroscience and behavioral biology.