UID:
edocfu_9958090672202883
Format:
1 online resource (307 p.)
ISBN:
1-283-52633-6
,
0-08-095762-5
Series Statement:
Studies in logic and the foundations of mathematics ; v. 42
Content:
Provability, Computability and Reflection
Note:
Description based upon print version of record.
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Front Cover; Non-Standard Analysis; Copyright Page; LIST OF CONTENTS; CHAPTER I. GENERAL INTRODUCTION; 1.1 Purpose of this book; 1.2 Summary of contents; CHAPTER II. TOOLS FROM LOGIC; 2.1 The Lower Predicate Calculus; 2.2 Interpretation; 2.3 Ultraproducts; 2.4 Prenex normal form; 2.5 The finiteness principle; 2.6 Higher order structures and corresponding languages; 2.7 Type symbols; 2.8 Finiteness principle for higher order theories; 2.9 Enlargements; 2.10 Examples of enlargements; 2.11 General properties of enlargements; 2.12 Remarks and references
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CHAPTER III. DIFFERENTIAL AND INTEGRAL CALCULUS3.1 Non-standard Arithmetic; 3.2 Non-standard Analysis; 3.3 Convergence; 3.4 Continuity and differentiation; 3.5 Integration; 3.6 Differentials; 3.7 Total differentials; 3.8 Elementary Differential Geometry; 3.9 Remarks and references; CHAPTER IV. GENERAL TOPOLOGY; 4.1 Topological spaces; 4.2 Sequences, nets, mappings; 4.3 Metric spaces; 4.4 Topologies in *T; 4.5 Functions, limits, continuity in metric spaces; 4.6 Sequences of functions, Compact mappings; 4.7 Euclidean space; 4.8 Remarks and references; CHAPTER V. FUNCTIONS OF A REAL VARlABLE
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5.1 Measure and integration5.2 Sequences of functions; 5.3 Distributions; 5.4 Remarks and references; CHAPTER VI. FUNCTIONS OF A COMPLEX VARIABLE; 6.1 Analytic theory of polynomials; 6.2 Analytic functions; 6.3 Picard's theorems and Julia's directions; 6.4 Compactness arguments in classical Function Theory; 6.5 Remarks and references; CHAPTER VII. LINEAR SPACES; 7.1 Normed spaces; 7.2 Hilbert space; 7.3 Spectral theory of compact operators; 7.4 An invariant subspace problem; 7.5 Remarks and references; CHAPTER VIIl. TOPOLOGICAL GROUPS AND LIE GROUPS; 8.1 Topological groups; 8.2 Metric groups
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8.3 One-parametric subgroups8.4 The Lie algebra of a group; 8.5 Remarks and references; CHAPTER IX. SELECTED TOPICS; 9.1 Variations; 9.2 Riemann's mapping theorem; 9.3 Dirichlet's principle; 9.4 Sources and doublets; 9.5 Local perturbations; 9.6 Boundary layer theory; 9.7 Saint-Venant's principle; 9.8 Remarks and references; CHAPTER X. CONCERNING THE HISTORY OF THE CALCULUS; 10.1 Introduction; 10.2 Leibniz; 10.3 De I'Hospital; 10.4 Lagrange and d'Alembert; 10.5 Cauchy; 10.6 Bolzano, Weierstrass. and after; 10.7 Infinitely small and large numbers and the infinite; BIBLIOGRAPHY
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INDEX OF AUTHORSSUBJECT INDEX
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English
Additional Edition:
ISBN 0-444-53407-5
Language:
English
