Format:
Online Ressource
ISBN:
9780444702661
,
0444705066
,
0444702660
,
0444703586
,
9780444703583
,
9780080570884
,
0080570887
Series Statement:
Studies in logic and the foundations of mathematics v. 121
Content:
1. Informal arithmetic and primitive recursive functions2. Primitive recursive arithmetic PRA; 3. Intuitionistic first-order arithmetic HA; 4. Algorithms; 5. Some metamathematics of HA; 6. Elementary analysis and elementary inductive definitions; 7. Formalization of elementary recursion theory; 8. Intuitionistic second-order logic and arithmetic; 9. Higher-order logic and arithmetic; 10. Notes; Exercises; Chapter 4 Non-classical axioms; 1. Preliminaries; 2. Choice axioms; 3. Church's thesis; 4. Realizability; 5. Markov's principle; 6. Choice sequences and continuity axioms; 7. The fan theorem
Content:
5. NotesExercises; Bibliography; Index; List of symbols
Content:
8. Bar induction and generalized inductive definitions9. Uniformity principles and Kripke's schema; 10. Notes; Exercises; Chapter 5 Real numbers; 1. Introduction; 2. Cauchy reals and their ordering; 3. Arithmetic on R; 4. Completeness properties and relativization; 5. Dedekind reals; 6. Arithmetic of Dedekind reals and extended reals; 7. Two metamathematical digressions; 8. Notes; Exercises; Chapter 6 Some elementary analysis; 1. Intermediate-value and supremum theorems; 2. Differentiation and integration; 3. Consequences of WC-N and FAN; 4. Analysis in CRM: consequences of CT0, ECT0, MP
Content:
Constructivism in Mathematics Vol.1
Content:
Front Cover; Constructivism in Mathematics: An Introduction; Copyright Page; CONTENTS OF VOLUME I; Preface; Preliminaries; Chapter 1 Introduction; 1. Constructivism; 2. Constructivity; 3. Weak counterexamples; 4. A brief history of constructivism; 5. Notes; Exercises; Chapter 2 Logic; 1. Natural deduction; 2. Logic with existence predicate; 3. Relationships between classical and intuitionistic logic; 4. Hilbert-type systems; 5. Kripke semantics; 6. Completeness for Kripke semantics; 7. Definitional extensions; 8. Notes; Exercises; Chapter 3 Arithmetic
Note:
Includes bibliographical references and index. - Print version record
,
Front Cover; Constructivism in Mathematics: An Introduction; Copyright Page; CONTENTS OF VOLUME I; Preface; Preliminaries; Chapter 1 Introduction; 1. Constructivism; 2. Constructivity; 3. Weak counterexamples; 4. A brief history of constructivism; 5. Notes; Exercises; Chapter 2 Logic; 1. Natural deduction; 2. Logic with existence predicate; 3. Relationships between classical and intuitionistic logic; 4. Hilbert-type systems; 5. Kripke semantics; 6. Completeness for Kripke semantics; 7. Definitional extensions; 8. Notes; Exercises; Chapter 3 Arithmetic
,
1. Informal arithmetic and primitive recursive functions2. Primitive recursive arithmetic PRA; 3. Intuitionistic first-order arithmetic HA; 4. Algorithms; 5. Some metamathematics of HA; 6. Elementary analysis and elementary inductive definitions; 7. Formalization of elementary recursion theory; 8. Intuitionistic second-order logic and arithmetic; 9. Higher-order logic and arithmetic; 10. Notes; Exercises; Chapter 4 Non-classical axioms; 1. Preliminaries; 2. Choice axioms; 3. Church's thesis; 4. Realizability; 5. Markov's principle; 6. Choice sequences and continuity axioms; 7. The fan theorem
,
8. Bar induction and generalized inductive definitions9. Uniformity principles and Kripke's schema; 10. Notes; Exercises; Chapter 5 Real numbers; 1. Introduction; 2. Cauchy reals and their ordering; 3. Arithmetic on R; 4. Completeness properties and relativization; 5. Dedekind reals; 6. Arithmetic of Dedekind reals and extended reals; 7. Two metamathematical digressions; 8. Notes; Exercises; Chapter 6 Some elementary analysis; 1. Intermediate-value and supremum theorems; 2. Differentiation and integration; 3. Consequences of WC-N and FAN; 4. Analysis in CRM: consequences of CT0, ECT0, MP
,
5. NotesExercises; Bibliography; Index; List of symbols;
Additional Edition:
ISBN 0444702660
Additional Edition:
ISBN 0444705066
Additional Edition:
Erscheint auch als Druck-Ausgabe Troelstra, A.S. (Anne Sjerp) Constructivism in mathematics Amsterdam : North-Holland, 1988
Language:
English
Subjects:
Mathematics
Keywords:
Mathematik
;
Konstruktivismus
;
Electronic books
;
Electronic books
Author information:
Troelstra, Anne S. 1939-2019
Author information:
Dalen, Dirk van 1932-
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