Axiomatic Set TheoryThis clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition. |
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Table des matières
INTRODUCTION | 1 |
GENERAL DEVELOPMENTS | 14 |
RELATIONS AND FUNCTIONS | 57 |
EQUIPOLLENCE FINITE SETS AND CARDINAL NUMBERS | 91 |
FINITE ORDINALS AND DENUMERABLE SETS | 127 |
RATIONAL NUMBERS AND REAL NUMBERS | 159 |
TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC | 195 |
THE AXIOM OF CHOICE | 239 |
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Expressions et termes fréquents
abstraction addition appropriate asserts axiom of choice axiom schema basis bound cardinal numbers Cauchy sequence Chapter clear complete conclude conditional connected consider construction corresponding define definition denumerable domain empty equipollent equivalence establish example exercise existence fact finite cardinal finite sets formulation fractions function Give given Hence holds hypothesis idea identity immediate implies infer infinite integer introduced intuitive language less limit ordinal logic mathematics maximal element multiplication natural numbers non-empty notation Note notion object obvious operation pairs paradox partition preceding primitive proof proper Prove Theorem range rational numbers real numbers recursion relation replacement requires respect result satisfy schema of separation sequences of rational set theory similar simple subset Suppose symbols Theorem 27 transitive union unique variables virtue of Theorem well-orders whence