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Introduction to Mathematical Logic 6th edition [Kõva köide]

4.03/5 (74 hinnangut Goodreads-ist)
(Queens College, Flushing, New York, USA)
  • Formaat: Hardback, 514 pages, kõrgus x laius: 234x156 mm, kaal: 880 g, 28 Illustrations, black and white
  • Sari: Discrete Mathematics and Its Applications
  • Ilmumisaeg: 08-Jun-2015
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1482237725
  • ISBN-13: 9781482237726
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Introduction to Mathematical Logic 6th editionSuurem pilt
  • Formaat: Hardback, 514 pages, kõrgus x laius: 234x156 mm, kaal: 880 g, 28 Illustrations, black and white
  • Sari: Discrete Mathematics and Its Applications
  • Ilmumisaeg: 08-Jun-2015
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1482237725
  • ISBN-13: 9781482237726
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Teised raamatud sellest sooduspakkumisest: Taylor & Francis teadusraamatud International Student Editions hindadega
Püsilink: https://www.kriso.ee/db/9781482237726.html
Märksõnad:
The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.

The sixth edition incorporates recent work on Gödels second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.

Arvustused

Praise for the Fifth Edition"Since it first appeared in 1964, Mendelson's book has been recognized as an excellent textbook in the field This book rightfully belongs in the small, elite set of superb books that every computer science graduate, graduate student, scientist, and teacher should be familiar with." Computing Reviews

"Since its first edition, this fine book has been a text of choice for a beginners course on mathematical logic There are many fine books on mathematical logic, but Mendelsons textbook remains a sure choice for a first course for its clear explanations and organization" MAA Reviews

"[ This book] is the most concise and readable introductory text I have ever encountered I have pulled the ideas for many test questions from it over the years." Charles Ashbacher, Upper Iowa University Praise for the Fifth Edition"Since it first appeared in 1964, Mendelsons book has been recognized as an excellent textbook in the field. It is one of the most frequently mentioned texts in references and recommended reading lists This book rightfully belongs in the small, elite set of superb books that every computer science graduate, graduate student, scientist, and teacher should be familiar with." Computing Reviews, May 2010

"The following are the significant changes in this edition: A new section (3.7) on the order type of a countable nonstandard model of arithmetic; a second appendix, Appendix B, on basic modal logic, in particular on the normal modal logics K, T, S4, and S5 and the relevant Kripke semantics for each; an expanded bibliography and additions to both the exercises and to the Answers to Selected Exercises, including corrections to the previous version of the latter." J.M. Plotkin, Zentralblatt MATH 1173

"Since its first edition, this fine book has been a text of choice for a beginners course on mathematical logic. There are many fine books on mathematical logic, but Mendelsons textbook remains a sure choice for a first course for its clear explanations and organization: definitions, examples and results fit together in a harmonic way, making the book a pleasure to read. The book is especially suitable for self-study, with a wealth of exercises to test the readers understanding." MAA Reviews, December 2009

Preface xiii
Introduction xv
1 The Propositional Calculus
1(44)
1.1 Propositional Connectives: Truth Tables
1(5)
1.2 Tautologies
6(13)
1.3 Adequate Sets of Connectives
19(8)
1.4 An Axiom System for the Propositional Calculus
27(9)
1.5 Independence: Many-Valued Logics
36(3)
1.6 Other Axiomatizations
39(6)
2 First-Order Logic and Model Theory
45(108)
2.1 Quantifiers
45(8)
2.1.1 Parentheses
48(5)
2.2 First-Order Languages and Their Interpretations: Satisfiability and Truth: Models
53(13)
2.3 First-Order Theories
66(3)
2.3.1 Logical Axioms
66(1)
2.3.2 Proper Axioms
67(1)
2.3.3 Rules of Inference
67(2)
2.4 Properties of First-Order Theories
69(4)
2.5 Additional Metatheorems and Derived Rules
73(5)
2.5.1 Particularization Rule A4
74(1)
2.5.2 Existential Rule E4
74(4)
2.6 Rule C
78(4)
2.7 Completeness Theorems
82(11)
2.8 First-Order Theories with Equality
93(9)
2.9 Definitions of New Function Letters and Individual Constants
102(3)
2.10 Prenex Normal Forms
105(6)
2.11 Isomorphism of Interpretations: Categoricity of Theories
111(2)
2.12 Generalized First-Order Theories: Completeness and Decidability
113(10)
2.12.1 Mathematical Applications
117(6)
2.13 Elementary Equivalence: Elementary Extensions
123(5)
2.14 Ultrapowers: Nonstandard Analysis
128(12)
2.14.1 Reduced Direct Products
131(5)
2.14.2 Nonstandard Analysis
136(4)
2.15 Semantic Trees
140(6)
2.15.1 Basic Principle of Semantic Trees
142(4)
2.16 Quantification Theory Allowing Empty Domains
146(7)
3 Formal Number Theory
153(78)
3.1 An Axiom System
153(16)
3.2 Number-Theoretic Functions and Relations
169(5)
3.3 Primitive Recursive and Recursive Functions
174(18)
3.4 Arithmetization: Godel Numbers
192(13)
3.5 The Fixed-Point Theorem: Godel's Incompleteness Theorem
205(13)
3.6 Recursive Undecidability: Church's Theorem
218(10)
3.7 Nonstandard Models
228(3)
4 Axiomatic Set Theory
231(80)
4.1 An Axiom System
231(16)
4.2 Ordinal Numbers
247(13)
4.3 Equinumerosity: Finite and Denumerable Sets
260(10)
4.3.1 Finite Sets
265(5)
4.4 Hartogs' Theorem: Initial Ordinals---Ordinal Arithmetic
270(12)
4.5 The Axiom of Choice: The Axiom of Regularity
282(11)
4.6 Other Axiomatizations of Set Theory
293(18)
4.6.1 Morse---Kelley (MK)
293(1)
4.6.2 Zermelo---Fraenkel (ZF)
294(2)
4.6.3 The Theory of Types (ST)
296(1)
4.6.3.1 ST1 (Extensionality Axiom)
297(1)
4.6.3.2 ST2 (Comprehension Axiom Scheme)
297(1)
4.6.3.3 ST3 (Axiom of Infinity)
298(2)
4.6.4 Quine's Theories NF and ML
300(1)
4.6.4.1 NF1 (Extensionality)
300(1)
4.6.4.2 NF2 (Comprehension)
301(2)
4.6.5 Set Theory with Urelements
303(8)
5 Computability
311(68)
5.1 Algorithms: Turing Machines
311(6)
5.2 Diagrams
317(8)
5.3 Partial Recursive Functions: Unsolvable Problems
325(16)
5.4 The Kleene---Mostowski Hierarchy: Recursively Enumerable Sets
341(14)
5.5 Other Notions of Computability
355(18)
5.5.1 Herbrand---Godel Computability
355(7)
5.5.2 Markov Algorithms
362(11)
5.6 Decision Problems
373(6)
Appendix A Second-Order Logic 379(16)
Appendix B First Steps in Modal Propositional Logic 395(12)
Appendix C A Consistency Proof for Formal Number Theory 407(12)
Answers to Selected Exercises 419(32)
Bibliography 451(16)
Notations 467(6)
Index 473
Elliott Mendelson is professor emeritus at Queens College in Flushing, New York, USA. Dr. Mendelson obtained his bachelor's degree at Columbia University and his master's and doctoral degrees at Cornell University, and was elected afterward to the Harvard Society of Fellows. In addition to his other writings, he is the author of another CRC Press book Introducing Game Theory and Its Applications.