Author: Alfred TarskiPublisher: Elsevier
ISBN: 0444533788
Category : Decidability (Mathematical logic)
Languages : en
Pages : 109
Book Description
Undecidable Theories
Author: Alfred TarskiPublisher: Dover Books on Mathematics
ISBN: 9780486477039
Category : Mathematics
Languages : en
Pages : 0
Book Description
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
Author: Anita Burdman FefermanComputability Theory
Author: S. Barry CooperPublisher: CRC Press
ISBN: 1420057561
Category : Mathematics
Languages : en
Pages : 420
Book Description
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.
Mathematical Logic and Formalized Theories
Author: Robert L. RogersPublisher: Elsevier
ISBN: 1483257975
Category : Mathematics
Languages : en
Pages : 248
Book Description
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.
Decision Problems for Equational Theories of Relation Algebras
Author: H. AndrékaPublisher: American Mathematical Soc.
ISBN: 0821805959
Category : Mathematics
Languages : en
Pages : 146
Book Description
"We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract.
The Theory of Models
Author: J.W. AddisonPublisher: Elsevier
ISBN: 1483275345
Category : Mathematics
Languages : en
Pages : 513
Book Description
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.
Set Theory and Logic
Author: Robert R. StollPublisher: Courier Corporation
ISBN: 0486139646
Category : Mathematics
Languages : en
Pages : 516
Book Description
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.
Uncertainty and Undecidability in Twentieth-Century Literature and Literary Theory
Author: Mette Leonard HøegPublisher: Taylor & Francis
ISBN: 1000568547
Category : Literary Criticism
Languages : en
Pages : 347
Book Description
Undecidability is a fundamental quality of literature and constitutive of what renders some works appealing and engaging across time and in different contexts. This book explores the essential literary notion and its role, function and effect in late nineteenth- and twentieth-century literature and literary theory. The book traces the notion historically, providing a map of central theories addressing interpretative challenges and recalcitrance in literature and showing ‘theory of uncertainty’ to be an essential strand of literary theory. While uncertainty is present in all literature, and indeed a prerequisite for any stabilisation of meaning, the Modernist period is characterised by a particularly strong awareness of uncertainty and its subforms of undecidability, ambiguity, indeterminacy, etc. With examples from seminal Modernist works by Woolf, Proust, Ford, Kafka and Musil, the book sheds light on undecidability as a central structuring principle and guiding philosophical idea in twentieth-century literature and demonstrates the analytical value of undecidability as a critical concept and reading-strategy. Defining undecidability as a specific ‘sustained’ and ‘productive’ kind of uncertainty and distinguishing it from related forms, such as ambiguity, indeterminacy and indistinction, the book develops a systematic but flexible theory of undecidability and outlines a productive reading-strategy based on the recognition of textual and interpretive undecidability.
