These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature
Author(s): Anne S. Troelstra, Dirk van Dalen
Series: Studies in Logic and the Foundations of Mathematics 121
Publisher: North-Holland
Year: 1988
Content:
Edited by
Page ii
Copyright Page
Page iii
Dedication
Page iv
Preface
Pages vii-ix
A.S. Troelstra, D. van Dalen
Preliminaries
Pages xi-xv
Constructivism in Mathematics: Contents
Page xvii
Chapter 1 Introduction
Pages 1-33
Chapter 2 Logic
Pages 35-111
Chapter 3 Arithmetic
Pages 113-183
Chapter 4 Non-Classical Axioms
Pages 185-249
Chapter 5 Real Numbers
Pages 251-289
Chapter 6 Some Elementary Analysis
Pages 291-325
Bibliography
Pages 327-342
Index
Pages 343-351
List of Symbols
Pages 353-356
