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Author: Stephen Cole Kleene
Publisher: American Mathematical Soc.
Published: 1969
Total Pages: 110
ISBN-13: 0821812890
DOWNLOAD EBOOKThis monograph carries out the program which the author formulated in earlier work, the formalization of the theory of recursive functions of type 0 and 1 and of the theory of realizability.
Author: A. R. D. Mathias
Publisher: Springer
Published: 2006-11-15
Total Pages: 673
ISBN-13: 3540368841
DOWNLOAD EBOOKAuthor: A.S. Troelstra
Publisher: Elsevier
Published: 2014-06-28
Total Pages: 607
ISBN-13: 008095510X
DOWNLOAD EBOOKStudies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras. The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences. The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras. The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.
Author: Yiannis N. Moschovakis
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 607
ISBN-13: 1461228220
DOWNLOAD EBOOKThe volume is the outgrowth of a workshop with the same title held at MSRI in the week of November 13-17, 1989, and for those who did not get it, Logic from Computer Science is the converse of Logic in Computer Science, the full name of the highly successful annual LICS conferences. We meant to have a conference which would bring together the LICS commu nity with some of the more traditional "mathematical logicians" and where the emphasis would be on the flow of ideas from computer science to logic rather than the other way around. In a LICS talk, sometimes, the speaker presents a perfectly good theorem about (say) the A-calculus or finite model theory in terms of its potential applications rather than its (often more ob vious) intrinsic, foundational interest and intricate proof. This is not meant to be a criticism; the LICS meetings are, after all, organized by the IEEE Computer Society. We thought, for once, it would be fun to see what we would get if we asked the speakers to emphasize the relevance of their work for logic rather than computer science and to point out what is involved in the proofs. I think, mostly, it worked. In any case, the group of people represented as broad a selection of logicians as I have seen in recent years, and the quality of the talks was (in my view) exceptionally, unusually high. I learned a lot and (I think) others did too.
Author: Juha Oikkonen
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 317
ISBN-13: 1316739651
DOWNLOAD EBOOKSince 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 Lecture Notes in Logic series, is the proceedings of the Association for Symbolic Logic meeting held in Helsinki, Finland, in July 1990. It contains eighteen papers by leading researchers, covering all fields of mathematical logic from the philosophy of mathematics, through model theory, proof theory, recursion theory, and set theory, to the connections of logic to computer science. The articles published here are still widely cited and continue to provide ideas for ongoing research projects.
Author: Al'bert Grigor'evi_ Dragalin
Publisher: American Mathematical Soc.
Published: 1988-12-31
Total Pages: 242
ISBN-13: 0821845209
DOWNLOAD EBOOKIn the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.
Author: W. Buchholz
Publisher: Springer
Published: 2006-11-14
Total Pages: 389
ISBN-13: 3540386491
DOWNLOAD EBOOKAuthor: Rohit Parikh
Publisher: Springer Science & Business Media
Published: 1985-06
Total Pages: 434
ISBN-13: 9783540156482
DOWNLOAD EBOOKAuthor: Lev D. Beklemishev
Publisher: Elsevier
Published: 2000-04-01
Total Pages: 525
ISBN-13: 0080954731
DOWNLOAD EBOOKIntuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo N.Y. 1968
Author: Leon Horsten
Publisher: Oxford University Press
Published: 2016-09-08
Total Pages: 272
ISBN-13: 0191077690
DOWNLOAD EBOOKThe logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
