Kooperativer Bibliotheksverbund

UID:

Format: 1 online resource (379 p.)

ISBN: 9780674042421

Note: Frontmatter -- , PREFACE TO THE REVISED EDITION -- , PREFACE TO THE FIRST EDITION -- , CONTENTS -- , INTRODUCTION -- , PART ONE THE ELEMENTS -- , I LOGIC -- , II REAL CLASSES -- , III CLASSES OF CLASSES -- , IV NATURAL NUMBERS -- , V ITERATION AND ARITHMETIC -- , PART TWO HIGHER FORMS OF NUMBER -- , VI REAL NUMBERS -- , VII ORDER AND ORDINALS -- , VIII TRANSFINITE RECURSION -- , IX CARDINAL NUMBERS -- , X THE AXIOM OF CHOICE -- , PART THREE AXIOM SYSTEMS -- , XI RUSSELL'S THEORY OF TYPES -- , XII GENERAL VARIABLES AND ZERMELO -- , XIII STRATIFICATION AND ULTIMATE CLASSES -- , XIV VON NEUMANN'S SYSTEM AND OTHERS -- , SYNOPSIS OF FIVE AXIOM SYSTEMS -- , LIST OF NUMBERED FORMULAS -- , BIBLIOGRAPHICAL REFERENCES -- , INDEX , In English.

Language: English

DOI: 10.4159/9780674042421

URL: https://doi.org/10.4159/9780674042421

URL: https://www.degruyter.com/isbn/9780674042421

UID:

Format: 1 online resource (361p.)

Edition: Rev. ed.

ISBN: 0-674-04242-5

Note: Previous ed. 1964. , Bibliographyp.343-351. _ Includes index. , INTRODUCTION PART ONE. THE ELEMENTS I. LOGIC Quantification and identity Virtual classes Virtual relations II. REAL CLASSES Reality, extensionality, and the individual The virtual amid the real Identity and substitution III. CLASSES OF CLASSES Unit classes Unions, intersections, descriptions Relations as classes of pairs Functions IV. NATURAL NUMBERS Numbers unconstrued Numbers construed Induction V. ITERATION AND ARITHMETIC Sequences and iterates The ancestral Sum, product, power PART TWO. HIGHER FORMS OF NUMBER VI. REAL NUMBERS Program. Numerical pairs Ratios and reals construed Existential needs. Operations and extensions VII. ORDER AND ORDINALS Transfinite induction Order Ordinal numbers Laws of ordinals The order of the ordinals VIII. TRANSFINITE RECURSION Transfinite recursion Laws of transfinite recursion Enumeration IX. CARDINAL NUMBERS Comparative size of classes The SchrOder-Bernstein theorem Infinite cardinal numbers X. THE AXIOM OF CHOICE Selections and selectors Further equivalents of the axiom The place of the axiom PART THREE. AXIOM SYSTEMS XI. RUSSELL'S THEORY OF TYPES The constructive part Classes and the axiom of reducibility The modern theory of types XII. GENERAL VARIABLES AND ZERMELO The theory of types with general variables Cumulative types and Zermelo Axioms of infinity and others XIII. STRATIFICATION AND ULTIMATE CLASSES "New foundations" Non-Cantorian classes. Induction again Ultimate classes added XIV. VON NEUMANN'S SYSTEM AND OTHERS The von Neumann-Bernays system Departures and comparisons Strength of systems SYNOPSIS OF FIVE AXIOM SYSTEMS LIST OF NUMBERED FORMULAS BIBLIOGRAPHICAL REFERENCES INDEX , English

Additional Edition: ISBN 0-674-80206-3

Additional Edition: ISBN 0-674-80207-1

Language: English

DOI: 10.4159/9780674042421