We solve a problem posed by Goncharov and Knight 639–681, 757]). More specifically, we produce an effective Friedberg enumeration of computable equivalence structures, up to isomorphism. We also prove that there exists an effective Friedberg enumeration of all isomorphism types of infinite computable equivalence structures.

A splitting A1A2 = A of an r.e. set A is called a Friedberg splitting if for any r.e. set W with W — A not r.e., W — Ai≠0 for I = 1,2. In an earlier paper, the authors investigated Friedberg splittings of maximal sets and showed that they formed an orbit with very interesting degree-theoretical properties. In the present paper we continue our investigations, this time analyzing Friedberg splittings and in particular their orbits and degrees (...) for various classes of r.e. sets. (shrink)

Keywords: Recursively Enumerable; Computably Enumerable; Friedberg Splitting; Congruence Relation; Ideal; Quotient; Lattice.

We define a property R(A 0 , A 1 ) in the partial order E of computably enumerable sets under inclusion, and prove that R implies that A 0 is noncomputable and incomplete. Moreover, the property is nonvacuous, and the A 0 and A 1 which we build satisfying R form a Friedberg splitting of their union A, with A 1 prompt and A promptly simple. We conclude that A 0 and A 1 lie in distinct orbits under automorphisms (...) of E, yielding a strong answer to a question previously explored by Downey, Stob, and Soare about whether halves of Friedberg splittings must lie in the same orbit. (shrink)

§1. Introduction. Natural sets that can be enumerated by a computable function always seem to be either actually computable or of the same complexity as the Halting Problem, the complete r.e. set K. The obvious question, first posed in Post [1944] and since then called Post's Problem is then just whether there are r.e. sets which are neither computable nor complete, i.e., neither recursive nor of the same Turing degree as K?Let be the r.e. degrees, i.e., the r.e. sets modulo (...) the equivalence relation of equicomputable with the partial order induced by Turing computability. This structure is a partial order with least element 0, the degree of the computable sets, and greatest element 1 or 0′, the degree of K. Post's problem then asks if there are any other elements of.The solution of Post's problem by Friedberg [1957] and Muchnik [1956] was followed by various algebraic or order theoretic results that were interpreted as saying that the structure was in some way well behaved:Theorem 1.1. Every countable partial ordering or even uppersemilattice can be embedded into.Theorem 1.2. For every nonrecursive r.e. degreeathere are r.e. degreesb, c < asuch thatb ∨ c = a.Theorem 1.3. For every pair of nonrecursive r.e. degreesa < bthere is an r.e. degreecsuch thata < c < b. (shrink)

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called “microscopic theory”, applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which (...) serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen–Specker–Bell theorem and Gleason’s theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory. (shrink)

This article is intended to emphasize several ethical issues relating to the activities of the internal auditor. The points of view expressed relate mainly to the public sector of Israel. Beyond the discussion of the specific issues against its unique Israeli background (Internal Audit Law), the discussion throws light on general problems that have not yet been solved.

A commentary on “Patient-Satisfaction Surveys on a Scale of 0 to 10: Improving Health Care, or Leading It Astray?,” byAlexandra Junewicz and Stuart J. Youngner in the May-June 2015 issue.

Eukaryotic cells are able to mount several genetically complex cellular responses to DNA damage. The yeast Saccharomyces cerevisiae is a genetically well characterized organism that is also amenable to molecular and biochemical studies. Hence, this organism has provided a useful and informative model for dissecting the biochemistry and molecular biology of DNA repair in eukaryotes.

Do we have free will? Can we trust our memories? How well do you know yourself? Felix Friedberg answers these questions in Caveat Homo Sapiens, arguing that humanity, while limited by the non-existence of free will, gains salvation in the ability to respond. Subjectivity, memory, psychotropic drugs, and the existence of the subconscious mind are explored, especially concerning their impact on self-knowledge and perception. Accessible to the general educated reader, the book will also be of interest to psychiatrists, sociologists (...) and philosophers. (shrink)

The advent of the post-Stalin "thaw," particularly the period after 1956, was marked by a spectacular expansion in the publishing of translated Western writing and also, on occasion, of editions in the original languages: the virtual ban on import of Western books was, as of 1975, never relaxed. The more permissive political atmosphere favored the publication of a vastly larger variety of Western authors and titles and provision for the Soviet public of much larger quantities of such books in the (...) country's bookstores and libraries. While the improvement was very impressive in itself, abundant data attest that it was far from adequate to satisfy reader demand.1 Among the beneficiaries, books by American authors stood out the more prominently since it was these that were most discriminated against during the years immediately preceding.2 Decades of neglect, to say nothing of politically inspired selectivity, resulted in such incongruities as the first Russian translation of Melville's Moby Dick in 1961—more than a century after the novel's appearance—and the first Soviet publication of any work by Henry James in 1973. It was not until the 1960's that Russians had an opportunity to read Faulkner—but then, the same was true of Kafka. However unevenly, the range of American literature, both old and new, now made available to Soviet readers is gradually expanding. · 1. The overall problem is discussed in detail in this writer's forthcoming book, A Decade of Euphoria: Western Literature in Post-Stalin Russia, 1954-64 . · 2. For a thorough and illuminating discussion of the fate of American literature in the U.S.S.R. from the Revolution until the early post-Stalin years, see Deming Brown, Soviet Attitudes toward American Writing . Interesting statistical data on the first post-Stalin years may also be found in Melville J. Ruggles, "American Books in Soviet Publishing," Slavic Review 20, n.3 : 419-35. A useful, very brief list of selected works of American writing published by 1968, though not entirely as complete as it purports to be, may be found in M.O. Mendel'son, A.N. Nikolyukin, R.M. Samarin, eds., Problemy literature S. Sh. A. XX. veka , pp. 391-517. Unfortunately, the Soviet bibliography contains no information on press runs of the books listed. Maurice Friedberg, head of the Department of Slavic Languages and Literatures at the University of Illinois, is the author of numerous essays and articles on Soviet literature. Professor Friedberg's most recent book, A Decade of Euphoria: Western Literature in Post-Stalin Russia, 1954-1964, will be published this year. (shrink)

Cockayne syndrome is a rare autosomal recessive disease characterized by a complex clinical phenotype. Most Cockayne syndrome cells are hypersensitive to killing by ultraviolet radiation. This observation has prompted a wealth of studies on the DNA repair capacity of Cockayne syndrome cells in vitro. Many studies support the notion that such cells are defective in a DNA repair mode(s) that is transcription‐dependent. However, it remains to be established that this is a primary molecular defect in Cockayne syndrome cells and that (...) it explains the complex clinical phenotype associated with the disease. An alternative hypothesis is that Cockayne syndrome cells have a defect in transcription affecting the expression of certain genes, which is compatible with embryogenesis but not with normal post‐natal development. Defective transcription may impair the normal processing of DNA damage during transcription‐dependent repair.‘“Curiouser and curiouser” cried Alice.’ (Lewis Carroll, Alice's Adventures in Wonderland). (shrink)

The study focuses on the links between gender and national security in the legislative arena in Israel, considering whether men and women legislators prioritize security differently, alongside other thematic policy areas. The centrality of national security issues in Israeli politics makes it a good case study for these questions, as it enhances existing gendered stereotypes. The article examines two competing hypotheses. The first suggests that Israeli female legislators will mostly refrain from addressing national security policy issues, focusing instead on softer (...) policy issues, such as gender equality, education, health, and welfare. The second suggests the opposite, claiming that women legislators in Israel will align themselves with their male counterparts’ set of priorities, focusing heavily on issues related to national security. The study finds support mostly for the former: Israeli female legislators are especially active in policy areas relating to women’s issues and children/family and are less active in regard to national security, a policy area heavily dominated by male legislators. (shrink)

The skin‐cancer‐prone hereditary disease xeroderma pigmentosum is typically characterized by defective nucleotide excision repair (NER) of DNA. However, since all subunits of the core basal transcription factor TFIIH are required for both RNA polymerase II basal transcription and NER, some mutations affecting genes that encode TFIIH subunits can result in clinical phenotypes associated with defective basal transcription. Among these is a syndrome called trichothiodystrophy (TTD) in which the prominent features are brittle hair and nails, and dry scaly skin. A recent (...) study provides dramatic support for the so‐called transcription hypothesis of TTD.(1) Specifically, several patients have been shown to carry a mutation in the XPD gene, which encodes a thermolabile form of XPD protein, resulting in loss of hair during febrile episodes. BioEssays 23:671–673, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

This article examines the relationship between online dispute resolution (ODR) and trust. We discuss what trust is, why trust is important, and how trust develops. Our claim is that efforts to implement online dispute resolution on a site or service in a manner that promotes trust need to consider ODR as just one tool in a broader toolbox of trust-building tools and techniques. These techniques are amongst others marketing, education, trust seals, and transparency. By evaluating ODR in its proper context (...) as one component of a larger trust strategy, we can more accurately set expectations for its results and position our projects for success. (shrink)

Let K be a family of structures, closed under isomorphism, in a fixed computable language. We consider effective lists of structures from K such that every structure in K is isomorphic to exactly one structure on the list. Such a list is called a computable classification of K, up to isomorphism. Using the technique of Friedberg enumeration, we show that there is a computable classification of the family of computable algebraic fields and that with a 0'-oracle, we can (...) obtain similar classifications of the families of computable equivalence structures and of computable finite-branching trees. However, there is no computable classification of the latter, nor of the family of computable torsion-free abelian groups of rank 1, even though these families are both closely allied with computable algebraic fields. (shrink)

The ethics research community has all but ignored issues of oversight ethics – the vices and virtues of overseers. This study develops a conceptual framework for exploring the ethics of oversight and provides insights into the design of codes of ethics for oversight institutions and for overseers. Analysis of business licensing in Israel reveals prospective and retrospective oversight ethics problems at the levels of national and local policy and implementation: Overseers failed to act on knowledge of breaches of business licensing (...) stipulations and took action known to be slow and ineffective; policymakers neglected their duty to enact significant policy change in an oversight system that was clearly not working. Partially as a result of these oversight failures, over one third of Israeli businesses are unlicensed, 23 people were killed in the collapse of an unlicensed banquet hall, 2 major fires erupted in the same shopping mall, and a fire in a fertilizer warehouse very nearly became a mega-disaster. (shrink)

We formulate an abstract version of the finite injury method in the form of the Baire category theorem. The theorem has the following corollaries: The Friedberg-Muchnik pair of recursively enumerable degrees, the Sacks splitting theorem, the existence of a minimal degree below 0′ and the Shoenfield jump theorem.

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and PAC (...) reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: [email protected]: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

We show that for every ordinal notation ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\xi}$$\end{document} of a nonzero computable ordinal, there exists a Σξ-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{-1}_\xi}$$\end{document}—computable family which up to equivalence has exactly one Friedberg numbering, which does not induce the least element in the corresponding Rogers semilattice.

We study a strong enumeration reducibility, called bounded enumeration reducibility and denoted by ≤be, which is a natural extension of s-reducibility ≤s. We show that ≤s, ≤be, and enumeration reducibility do not coincide on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} –sets, and the structure \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\mathcal{D}_{\rm be}}}$$\end{document} of the be-degrees is not elementarily equivalent to the structure of the s-degrees. We show also that the (...) first order theory of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\mathcal{D}_{\rm be}}}$$\end{document} is computably isomorphic to true second order arithmetic: this answers an open question raised by Cooper (Z Math Logik Grundlag Math 33:537–560, 1987). (shrink)