Axiomatic Set TheoryCourier Corporation, 4 mai 2012 - 265 pages One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: "Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?" Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. |
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... sets, finite sets and cardinal numbers. The Schröder-Bernstein Theorem is proved early in the chapter. The development of the theory of finite sets follows closely Alfred Tarski's well known article of 1924. The theory of cardinal ...
... sets of the power of the continuum are proved in the final section. Because ... sets are proved in the latter part of the chapter. Chapter 8 deals mainly with the axiom of choice and its ... finite cardinals. The material in the first six.
Patrick Suppes. numbers as finite cardinals. The material in the first six chapters, ending with the construction of the real numbers, is suitable for an undergraduate mathematics course in the foundations of analysis, or as auxiliary ...
... Equipollence 4.2 Finite Sets 4.3 Cardinal Numbers 4.4 Finite Cardinals 5. FINITE ORDINALS AND DENUMERABLE SETS 5.1 Definition and General Properties of Ordinals 5.2 Finite Ordinals and Recursive Definitions 5.3 Denumerable Sets 6.
Patrick Suppes. 5.2 Finite Ordinals and Recursive Definitions 5.3 Denumerable Sets 6. RATIONAL NUMBERS AND REAL NUMBERS 6.1 Introduction 6.2 Fractions 6.3 Non-negative Rational Numbers 6.4 Rational Numbers 6.5 Cauchy Sequences of ...
Table des matières
RELATIONS AND FUNCTIONS | |
EQUIPOLLENCE FINITE SETS AND CARDINAL NUMBERS | |
FINITE ORDINALS AND DENUMERABLE SETS | |
RATIONAL NUMBERS AND REAL NUMBERS | |
TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC | |
THE AXIOM OF CHOICE | |
REFERENCES | |
AUTHOR INDEX | |