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Author : Alfred Tarski,Andrzej Mostowski,Raphael Mitchel Robinson
Publisher : Elsevier
Page : 109 pages
File Size : 49,6 Mb
Release : 1953
Category : Decidability (Mathematical logic)
ISBN : 9780444533784
Author : Alfred Tarski,Andrzej Mostowski,Raphael M. Robinson
Publisher : Dover Books on Mathematics
Page : 0 pages
File Size : 41,8 Mb
Release : 2010
Category : Mathematics
ISBN : 0486477037
This well-known book by the famed logician consists of three treatises: A General Method in Proofs of Undecidability, Undecidability and Essential Undecidability in Mathematics, and Undecidability of the Elementary Theory of Groups. 1953 edition.
Author : Dirk Siefkes
Publisher : Springer
Page : 142 pages
File Size : 51,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540362524
Author : Alfred Tarski
Publisher : Unknown
Page : 120 pages
File Size : 41,9 Mb
Release : 1968
Category : Gödel's theorem
ISBN : UCSD:31822013430483
Author : Anita Burdman Feferman,Solomon Feferman
Publisher : Cambridge University Press
Page : 442 pages
File Size : 49,5 Mb
Release : 2004-10-04
Category : Mathematics
ISBN : 0521802407
Publisher Description
Author : S. Barry Cooper
Publisher : CRC Press
Page : 420 pages
File Size : 46,8 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781420057560
Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.
Author : Robert L. Rogers
Publisher : Elsevier
Page : 248 pages
File Size : 45,8 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483257976
Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.
Author : H. Andréka,Steven R. Givant,I. Németi
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 45,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805954
This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.
Author : J.W. Addison,Leon Henkin,Alfred Tarski
Publisher : Elsevier
Page : 513 pages
File Size : 42,6 Mb
Release : 2014-05-27
Category : Mathematics
ISBN : 9781483275345
Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.
Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 51,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author : Alfred Taski
Publisher : Unknown
Page : 98 pages
File Size : 50,6 Mb
Release : 1973
Category : Electronic
ISBN : OCLC:318168652
Author : Ralph McKenzie,Matthew Valeriote
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461245520
A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [1931] paper on formally undecidable propo sitions of arithmetic. During the 1930s, in the work of such mathemati cians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church pro posed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)-i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The de termination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A.
Author : Lev D. Beklemishev
Publisher : Elsevier
Page : 109 pages
File Size : 44,8 Mb
Release : 2000-04-01
Category : Computers
ISBN : 9780080957333
Provability, Computability and Reflection
Author : D. P. Acharjya
Publisher : MJP Publisher
Page : 416 pages
File Size : 55,9 Mb
Release : 2019-06-12
Category : Science
ISBN : 8210379456XXX
Theory of computation is the scientific discipline concerned with the study of general properties of computation and studies the inherent possibilities and limitations of efficient computation that makes machines more intelligent and enables them to carry out intellectual processes. This book deals with all those concepts by developing the standard mathematical models of computational devices, and by investigating the cognitive and generative capabilities of such machines. The book emphasizes on mathematical reasoning and problem-solving techniques that penetrate computer science. Each chapter gives a clear statement of definition and thoroughly discusses the concepts, principles and theorems with illustrative and other descriptive materials.
Author : Anonim
Publisher : Elsevier
Page : 619 pages
File Size : 48,6 Mb
Release : 1998-11-30
Category : Computers
ISBN : 0080533698
Recursive Model Theory
