Title Computability Theory and Its Applications : Current Trends and Open Problems

Published Providence : American Mathematical Society, 2000

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Description 1 online resource (338 pages) Series Contemporary Mathematics ; v. 257 Contemporary Mathematics Contents Contents -- Preface -- Program of invited talks -- Conference participants -- Randomness in computability theory -- Open questions about the n-c.e. degrees -- The theory of numberings: Open problems -- Π01 classes � structure and applications -- The global structure of computably enumerable sets -- Computability theory in arithmetic: Provability, structure and techniques -- How many Turing degrees are there? -- Questions in computable algebra and combinatorics -- Issues and problems in reverse mathematics -- 1. The Emergence of Reverse Mathematics 2. The Reverse Mathematics Enterprise3. The Interpretability Conjecture -- 4. The Coding Issue -- 5. Real Analysis and Topology -- 6. Banach Space Theory -- 7. Ramsey Theory -- 8. WQO Theory -- 9. Countable Abelian Group Theory -- 10. Replacing RCA0 by a Weaker Base Theory -- References -- Open problems in the theory of constructive algebraic systems -- Independence results from ZFC in computability theory: Some open problems -- Problems related to arithmetic -- Embeddings into the computably enumerable degrees Definability in the c.e. degrees: Questions and resultsStrong reducibilities, again -- Finitely axiomatizable theories and Lindenbaum algebras of semantic classes -- Towards an analog of Hilbert's tenth problem for a number field -- Natural definability in degree structures -- Recursion theory in set theory -- Extensions, automorphisms, and definability -- Open problems in the enumeration degrees Bibliography Includes bibliographical references Notes English Print version record Subject Computable functions -- Congresses Computable functions Genre/Form Conference papers and proceedings Form Electronic book Author Lempp, Steffen Lerman, Manuel ISBN 9780821878477 0821878476 9780821855935 082185593X

Other Titles Contemporary Mathematics Contemporary Mathematics, Volume 257 Computability theory and its applications: current trends and open problems : proceedings of a 1999 AMS-IMS-SIAM joint summer research conference, computability theory and applications, June 13-17, 1999, University of Colorado, Boulder

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