Search results for: techniques-of-admissible-recursion-theory

Techniques of Admissible Recursion Theory

Author : C. T. Chong
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Techniques of Admissible Recursion Theory

Author : C. T. Chong
File Size : 35.64 MB
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Higher Recursion Theory

Author : Gerald E. Sacks
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, α-recursion, and E-recursion. This text is essential reading for all researchers in the field.

Computability Theory And Foundations Of Mathematics Proceedings Of The 9th International Conference On Computability Theory And Foundations Of Mathematics

Author : Ningning Peng
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This volume features the latest scientific developments in the fields of computability theory and logical foundations of mathematics as well as applications. The scope involves the topics of Computability Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Theory of Randomness and Computational Complexity Theory.

Handbook of Computability Theory

Author : E.R. Griffor
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The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.

The Role of True Finiteness in the Admissible Recursively Enumerable Degrees

Author : Noam Greenberg
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When attempting to generalize recursion theory to admissible ordinals, it may seem as if all classical priority constructions can be lifted to any admissible ordinal satisfying a sufficiently strong fragment of the replacement scheme. We show, however, that this is not always the case. In fact, there are some constructions which make an essential use of the notion of finiteness which cannot be replaced by the generalized notion of $\alpha$-finiteness. As examples we discuss both codings of models of arithmetic into the recursively enumerable degrees, and non-distributive lattice embeddings into these degrees. We show that if an admissible ordinal $\alpha$ is effectively close to $\omega$ (where this closeness can be measured by size or by cofinality) then such constructions may be performed in the $\alpha$-r.e. degrees, but otherwise they fail. The results of these constructions can be expressed in the first-order language of partially ordered sets, and so these results also show that there are natural elementary differences between the structures of $\alpha$-r.e. degrees for various classes of admissible ordinals $\alpha$. Together with coding work which shows that for some $\alpha$, the theory of the $\alpha$-r.e. degrees is complicated, we get that for every admissible ordinal $\alpha$, the $\alpha$-r.e. degrees and the classical r.e. degrees are not elementarily equivalent.

Recursion Theory Week

Author : Heinz-Dieter Ebbinghaus
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Classical Recursion Theory

Author : P. Odifreddi
File Size : 83.94 MB
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1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.

General Recursion Theory

Author : Jens E. Fenstad
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This volume presents a unified and coherent account of the many and various parts of general recursion theory.

Proceedings of the 13th Asian Logic Conference

Author : Xishun Zhao
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This volume provides a forum which highlights new achievements and overviews of recent developments of the thriving logic groups in the Asia-Pacific region. It contains papers by leading logicians and also some contributions in computer science logics and philosophic logics. Contents:An Analogy Between Cardinal Characteristics and Highness Properties of Oracles (Jörg Brendle, Andrew Brooke-Taylor, Keng Meng Ng and André Nies)A Non-Uniformly C-Productive Sequence & Non-Constructive Disjunctions (John Case, Michael Ralston and Yohji Akama)Minimal Pairs in the C. E. Truth-Table Degrees (Rod Downey and Keng Meng Ng)A Survey on Recent Results on Partial Learning (Ziyuan Gao, Sanjay Jain, Frank Stephan and Sandra Zilles)Characterization of the Second Homology Group of a Stationary Type in a Stable Theory (John Goodrick, Byunghan Kim and Alexei Kolesnikov)Some Questions Concerning Ab Initio Generic Structures (Koichiro Ikeda)Model Complete Generic Structures (Koichiro Ikeda and Hirotaka Kikyo)On Categorical Relationship among Various Fuzzy Topological Systems, Fuzzy Topological Spaces and Related Algebraic Structures (Purbita Jana and Mihir K Chakraborty)Realizability and Existence Property of a Constructive Set Theory with Types (Farida Kachapova)Goal-Directed Unbounded Coalitional Game and Its Complexity (Hu Liu)On Extensions of Basic Propositional Logic (Minghui Ma and Katsuhiko Sano)Large Cardinals and Higher Degree Theory (Xianghui Shi)Degree Spectra of Equivalence Relations (Liang Yu) Readership: Researchers in mathematical logic and algebra, computer scientists in artificial intelligence and fuzzy logic. Key Features:The Asian Logic Conference is the most significant logic meeting outside of North America and EuropeThe contributors are prominent logicians or young leading researchersSome papers propose a few new questions or new research topicsKeywords:Mathematical Logic;Recursion Theory;Axiomatic Set Theory;Model Theory;Computability;Degree;Forcing;Large Cardinal;Generic Structure;Algebraic Structure;Philosophic Logic