Ambos-Spies, K. and R.A. Shore, Undecidability and 1-types in the recursively enumerable degrees, Annals of Pure and Applied Logic 63 3–37. We show that the theory of the partial ordering of recursively enumerable Turing degrees is undecidable and has uncountably many 1-types. In contrast to the original proof of the former which used a very complicated O''' argument our proof proceeds by a much simpler infinite injury argument. Moreover, it combines with the permitting technique to get similar results (...) for any ideal of the r.e. degrees. (shrink)

In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0.

We show that the partial order of Σ0 3-sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi.

A recursively enumerable splitting of an r.e. setAis a pair of r.e. setsBandCsuch thatA=B∪CandB∩C= ⊘. Since for such a splitting degA= degB∪ degC, r.e. splittings proved to be a quite useful notion for investigations into the structure of the r.e. degrees. Important splitting theorems, like Sacks splitting [S1], Robinson splitting [R1] and Lachlan splitting [L3], use r.e. splittings.Since each r.e. splitting of a set induces a splitting of its degree, it is natural to study the relation between the degrees of (...) r.e. splittings and the degree splittings of a set. We say a setAhas thestrong universal splitting property if each splitting of its degree is represented by an r.e. splitting of itself, i.e., if for degA=b∪cthere is an r.e. splittingB, CofAsuch that degB=band degC=c. The goal of this paper is the study of this splitting property.In the literature some weaker splitting properties have been studied as well as splitting properties which imply failure of the SUSP. (shrink)

We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.

It is shown that, if a, b are recursively enumerable degrees such that 0

Logic and Philosophy of Logic

Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic

Model Theory in Logic and Philosophy of Logic

Direct download (4 more)  

 

Export citation  

 

Bookmark   6 citations  

Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides with (...) local nonmodularity in the computably enumerable degrees. (shrink)

We give a simple structural property which characterizes the r.e. sets whose (Turing) degrees are cappable. Since cappable degrees are incomplete, this may be viewed as a solution of Post's program, which asks for a simple structural property of nonrecursive r.e. sets which ensures incompleteness.

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...) disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier theory. These criteria are applied not only to the weak truth-table degrees of the recursively enumerable sets but also to various substructures of the polynomial many-one (pm) degrees of the recursive sets. These applications to the pm degrees require no new complexity-theoretic results. The fact that the pm-degrees of the recursive sets have a decidable two-quantifier theory answers a question raised by Shore and Slaman in [21]. (shrink)

We show that, in the partial ordering of the computably enumerable computable Lipschitz degrees, there is a degree a>0a>0 such that the class of the degrees which do not cup to a is not bounded by any degree less than a. Since Ambos-Spies [1] has shown that, in the partial ordering of the c.e. identity-bounded Turing degrees, for any degree a>0a>0 the degrees which do not cup to a are bounded by the 1-shift a+1a+1 of a where a+1 (...) it follows that the elementary theories of the partial orderings and differ. (shrink)

We explore the complexity of Sacks’ Splitting Theorem in terms of the mind change functions associated with the members of the splits. We prove that, for any c.e. set A, there are low computably enumerable sets $A_0\sqcup A_1=A$ splitting A with $A_0$ and $A_1$ both totally $\omega ^2$ -c.a. in terms of the Downey–Greenberg hierarchy, and this result cannot be improved to totally $\omega $ -c.a. as shown in [9]. We also show that if cone avoidance is added then there (...) is no level below $\varepsilon _0$ which can be used to characterize the complexity of $A_1$ and $A_2$. (shrink)

We solve a longstanding question of Soare by showing that if ${\mathbf d}$ is a non-low $_2$ computably enumerable degree then ${\mathbf d}$ contains a c.e. set with no r-maximal c.e. superset.

We show that the theory of the partial ordering of the computably enumerable degrees in any given nontrivial interval is undecidable and has uncountably many 1-types.

In lieu of an abstract, here is a brief excerpt of the content:Diacritics 30.4 (2000) 59-82 [Access article in PDF] Bombing and the Symptom Traumatic Earliness and the Nuclear Uncanny Paul K. Saint-Amour Many used the Japanese word bukimi, meaning weird, ghastly, or unearthly, to describe Hiroshima's uneasy combination of continued good fortune and expectation of catastrophe. People remembered saying to one another, "Will it be tomorrow or the day after tomorrow?" One man described how, each night he was on (...) air-raid watch, "I trembled with fear.... I would think, "Tonight it will be Hiroshima." These "premonitions" were partly attempts at psychic preparation, partly a form of "imagining the worst" as a magical way of warding off disaster. —Robert J. Lifton, Death in Life: Survivors of Hiroshima (1967) Robert J. Lifton's pathbreaking work on the survivors of the atomic bombing of Hiroshima focuses on the psychological aftermath of the bomb, but opens with a brief and surprising section called "Anticipation." Given the instantaneous and unprecedented devastation caused by the first atomic bomb, the anticipation of so singular an experience is just as difficult to imagine as its subsequent assimilation. In fact, the unassimilable nature of traumatic violence would seem to depend in some way upon the impossibility of its anticipation, as Lifton implies: "Neither past experience nor immediate perceptions—the two sources of prior imagination—could encompass what was about to occur." Yet Lifton also records an expectant, premonitory atmosphere in Hiroshima during the weeks before the bombing, a compound of past experience and immediate perceptions that, while inadequate to "encompass" the eventual experience of the bomb, cannot simply be dismissed as speculation that found an accidental correlate in the nuclear event. While no one in Hiroshima knew ahead of time what would occur on August 6, 1945, many had noted the city's eerie exemption from conventional bombardment and speculated as to the reasons for it. During the summer of 1945, a series of rumors circulated in Hiroshima, rumors attributing the sparing of the city, variously, to its modest military and industrial significance; to the presence of prominent foreigners there, possibly including President Truman's mother; to important American prisoners-of-war supposedly held in the city; to the number of its citizens who had emigrated to the US; to the presence of large numbers of American spies living among its citizens; to its physical appeal in the eyes of Americans who had saved the city as a site for their postwar occupation villas; and, most wishfully, to the wartime grace of a cartographic error: "We thought that perhaps the city of Hiroshima was not on the American maps" [Lifton 15-17]. 1 Other inhabitants [End Page 59] of the city feared that Hiroshima appeared all too prominently on US maps, but had been set aside for "something unusually big"—perhaps the inundation of the city by floodwaters that could be released by the bombing of a massive upstream dam. Still others spoke of a "special bomb" [PWRS 220-22; Lifton 17]. All these rumors responded to citizens' impression that their city had been in some way singled out, and the term bukimi—also meaning "ominous" or "uncanny"—spoke to the suspended question of whether Hiroshima and its inhabitants had been singled out for preservation or for annihilation.The survivors who recollected their anticipatory bukimi years after the bombing may have retrospectively amplified their memories of weird expectation, perhaps as a way of attempting to master an incommensurable and singular event by installing it within a narrative of causality, continuity, even prophecy. Nonetheless, the bukimi experienced by inhabitants of Hiroshima should not be understood as pure retrospection, nor as groundless hunch, since it arose from a series of empirical observations later revealed to have a single and coherent origin in US military strategy. By the summer of 1945, most Japanese cities whose size and military-industrial importance were similar to Hiroshima's had already been bombed with incendiaries: those who lived in Hiroshima had watched waves of American bombers fly past on their way to other targets, while the dozen or so bombs that had fallen accidentally on... (shrink)

Very shortly before the end of Book 11 of the Aeneid, Turnus, hearing of Camilla's death, is forced to abandon his ambush in order to fall back to the city. Just after he leaves the wooded gorge, Aeneas passes through it unscathed with his company. Both then head toward the city walls. Virgil marks this near miss of the two commanders by an acrostic :ille furens deserit obsessos collis, nemora aspera linquit.uix e conspectu exierat campumque tenebat,cum pater Aeneas saltus ingressus (...) apertosexsuperatque iugum siluaque euadit opaca.sic ambo ad muros rapidi totoque ferunturagmine nec longis inter se passibus absunt. (shrink)

κάτοπτρον, which is in all the manuscripts, was emended by Canter to κάτοπτον, and this emendation, or Headlam's κατόπτην, has been received by subsequent editors. Those who read κάτοπτον have been in the habit of taking the word to mean here ‘looking down upon’, and in support of this interpretation they sometimes adduce a scholium in M, κατόψιον. This does seem to prove that the scholar, whose note is copied in our scholium, found κάτοπτον in his text. Presumably he took (...) Σαρωνικο πορθμο κάτοπτον to signify ‘descried from the Saronic gulf’, having very possibly in his mind the phrase in Euripides, Hippolytus 30, where the temple of Cypris is said to be κατόψιον γς τσδε, visible from Troezen. At least we ought not without proof to lay to his account what appears to be the solecism of regarding κάτοπτον as if it meant ‘looking down upon’. Headlam's κατόπτην has at least an active force, but I cannot find that it means ‘one who looks down upon’, if that is the sense desired; it is a ‘spy’ or an ‘inspector’. And, at the end of all discussion, when one asks what in fact is this peak or headland that ‘looks down upon the Saronic crossing’, then commentators take refuge in silence or tend to contradict one another. An emendation that nobody can be sure he understands can hardly be regarded as satisfactory. It may be feared that what has happened is this. In order to get rid of κάτοπτρον, which appeared to them devoid of meaning, editors have introduced into the text a word which does not mean what they want it to mean, and which, if it had that meaning, would still present us with a picture which no man can recognize. (shrink)

Objectives To conduct an independent evaluation of the first phase of the Health Foundation’s Safer Patients Initiative (SPI), and to identify the net additional effect of SPI and any differences in changes in participating and non-participating NHS hospitals. Design Mixed method evaluation involving five substudies, before and after design. Setting NHS hospitals in the United Kingdom. Participants Four hospitals (one in each country in the UK) participating in the first phase of the SPI (SPI1); 18 control hospitals. Intervention The SPI1 (...) was a compound (multi-component) organisational intervention delivered over 18 months that focused on improving the reliability of specific frontline care processes in designated clinical specialties and promoting organisational and cultural change. Results Senior staff members were knowledgeable and enthusiastic about SPI1. There was a small (0.08 points on a 5 point scale) but significant (P<0.01) effect in favour of the SPI1 hospitals in one of 11 dimensions of the staff questionnaire (organisational climate). Qualitative evidence showed only modest penetration of SPI1 at medical ward level. Although SPI1 was designed to engage staff from the bottom up, it did not usually feel like this to those working on the wards, and questions about legitimacy of some aspects of SPI1 were raised. Of the five components to identify patients at risk of deterioration—monitoring of vital signs (14 items); routine tests (three items); evidence based standards specific to certain diseases (three items); prescribing errors (multiple items from the British National Formulary); and medical history taking (11 items)—there was little net difference between control and SPI1 hospitals, except in relation to quality of monitoring of acute medical patients, which improved on average over time across all hospitals. Recording of respiratory rate increased to a greater degree in SPI1 than in control hospitals; in the second six hours after admission recording increased from 40% (93) to 69% (165) in control hospitals and from 37% (141) to 78% (296) in SPI1 hospitals (odds ratio for “difference in difference” 2.1, 99% confidence interval 1.0 to 4.3; P=0.008). Use of a formal scoring system for patients with pneumonia also increased over time (from 2% (102) to 23% (111) in control hospitals and from 2% (170) to 9% (189) in SPI1 hospitals), which favoured controls and was not significant (0.3, 0.02 to 3.4; P=0.173). There were no improvements in the proportion of prescription errors and no effects that could be attributed to SPI1 in non-targeted generic areas (such as enhanced safety culture). On some measures, the lack of effect could be because compliance was already high at baseline (such as use of steroids in over 85% of cases where indicated), but even when there was more room for improvement (such as in quality of medical history taking), there was no significant additional net effect of SPI1. There were no changes over time or between control and SPI1 hospitals in errors or rates of adverse events in patients in medical wards. Mortality increased from 11% (27) to 16% (39) among controls and decreased from 17% (63) to 13% (49) among SPI1 hospitals, but the risk adjusted difference was not significant (0.5, 0.2 to 1.4; P=0.085). Poor care was a contributing factor in four of the 178 deaths identified by review of case notes. The survey of patients showed no significant differences apart from an increase in perception of cleanliness in favour of SPI1 hospitals. Conclusions The introduction of SPI1 was associated with improvements in one of the types of clinical process studied (monitoring of vital signs) and one measure of staff perceptions of organisational climate. There was no additional effect of SPI1 on other targeted issues nor on other measures of generic organisational strengthening. (shrink)

The 1996 European Summer Meeting of the Association of Symbolic Logic was held held the University of the Basque Country, at Donostia (San Se bastian) Spain, on July 9-15, 1996. It was organised by the Institute for Logic, Cognition, Language and Information (ILCLI) and the Department of Logic and Philosophy of Sciences of the University of the Basque Coun try. It was supported by: the University of Pais Vasco/Euskal Herriko Unib ertsitatea, the Ministerio de Education y Ciencia (DGCYT), Hezkuntza Saila (...) (Eusko Jaurlaritza), Gipuzkoako Foru Aldundia, and Kuxta Fun dazioa. The main topics of the meeting were Model Theory, Proof Theory, Re cursion and Complexity Theory, Models of Arithmetic, Logic for Artifi cial Intelligence, Formal Semantics of Natural Language and Philosophy of Contemporary Logic. The Program Committee consisted of K. Ambos Spies (Heidelberg), J.L. Balcazar (Barcelona), J.E. Fenstad (Oslo), D. Israel (Stanford), H. Kamp (Stuttgart), R. Kaye (Birmingham), J.M. Larrazabal (San Sebastian), D. Lascar (Paris, chairman), A. Marcja (Firenze), G. Mints (Stanford), M. Otero (Madrid), S. Ronchi della Rocca (Torino), K. Segerberg (Uppsala) and L. Vega (Madrid). The organizing Committee consisted of X. Arrazola (San Sebastian), A. Arrieta (San Sebastian), R. Beneyeto (Valencia), B. Carrascal (San Se bastian), K. Korta (San Sebastian), J.M. Larrazabal (San Sebastian, chair man), J.C. Martinez (Barcelona), J.M. Mendez (Salamanca), F. Migura (Victoria) and J. Perez (Victoria). (shrink)

This is the first book to offer the best essays, articles, and speeches on ethics and intelligence that demonstrate the complex moral dilemmas in intelligence collection, analysis, and operations. Some are recently declassified and never before published, and all are written by authors whose backgrounds are as varied as their insights, including Robert M. Gates, former Director of the Central Intelligence Agency; John P. Langan, the Joseph Cardinal Bernardin Professor of Catholic Social Thought at the Kennedy Institute of Ethics, Georgetown (...) University; and Loch K. Johnson, Regents Professor of Political Science at the University of Georgia and recipient of the Owens Award for contributions to the understanding of U.S. intelligence activities. Creating the foundation for the study of ethics and intelligence by filling in the gap between warfare and philosophy, this is a valuable collection of literature for building an ethical code that is not dependent on any specific agency, department, or country. (shrink)

This is the first book to offer the best essays, articles, and speeches on ethics and intelligence that demonstrate the complex moral dilemmas in intelligence collection, analysis, and operations. Some are recently declassified and never before published, and all are written by authors whose backgrounds are as varied as their insights, including Robert M. Gates, former Director of the Central Intelligence Agency; John P. Langan, the Joseph Cardinal Bernardin Professor of Catholic Social Thought at the Kennedy Institute of Ethics, Georgetown (...) University; and Loch K. Johnson, Regents Professor of Political Science at the University of Georgia and recipient of the Owens Award for contributions to the understanding of U.S. intelligence activities. Creating the foundation for the study of ethics and intelligence by filling in the gap between warfare and philosophy, this is a valuable collection of literature for building an ethical code that is not dependent on any specific agency, department, or country. (shrink)

A partir de las propuestas metodológicas de los Estudios del Imaginario, este trabajo busca mostrar que algunas de las principales tramas ideadas por Philip K. Dick tienen un sustrato gnóstico. Para ello, en primer lugar, mencionamos algunos datos biográficos que muestran el interés de Dick por el gnosticismo; en segundo lugar, identificamos mitemas idénticos entre ambos corpus (“este mundo es un engaño”; “este mundo es una prisión de hierro”; “el iniciado tiene un doble”; etc.). Con ello, esta investigación contribuye (...) al debate científico en torno a la recepción y reutilización de antiguos mitos en la literatura de ciencia ficción. (shrink)

Studie se věnuje dialogu Anselma z Canterbury De grammatico. Tento spis byl samotným autorem označen jako úvod do dialektiky. V dobové dialektice zastával klíčové místo Aristotelův spis Kategorie. Tento článek se proto pokouší interpretovat Anselmův dialog jako určitou pedagogicky koncipovanou podobu komentáře k Aristotelovým Kategoriím. V návaznosti na Anselmův spis jsou postupně představeny jednotlivé teze z Aristotelových Kategorií (jak tzv. antepredicamenta, tak pojednání o substanci, kvalitě a částečně i vlastnictví) a způsob, jakým s nimi Anselm pracoval.

Studie se věnuje dialogu Anselma z Canterbury De grammatico. Tento spis byl samotným autorem označen jako úvod do dialektiky. V dobové dialektice zastával klíčové místo Aristotelův spis Kategorie. Tento článek se proto pokouší interpretovat Anselmův dialog jako určitou pedagogicky koncipovanou podobu komentáře k Aristotelovým Kategoriím. V návaznosti na Anselmův spis jsou postupně představeny jednotlivé teze z Aristotelových Kategorií (jak tzv. antepredicamenta, tak pojednání o substanci, kvalitě a částečně i vlastnictví) a způsob, jakým s nimi Anselm pracoval.