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Set Theory and the Continuum Problem

Raymond M. Smullyan (Autor)

Buch | Hardcover

301 Seiten

1996
Clarendon Press (Verlag)
978-0-19-852395-6 (ISBN)

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This text forms an introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know.

Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know. This book is intended for graduate students and researchers in mathematical logic.

Part I. General background. Some basics of class-set theory. The natural number. Superinduction, well ordering and choice. Ordinal numbers. Order isomorphism and transfinite recursion. Rank. Foundation, e-induction, and rank. Cardinals. Part II. Mostowski-Shepherdson Mappings. Reflection principles. Constructible sets. L is well founded first-order universe. Constructability is absolute over L. Constructability and the continuum hypothesis. Part III. Forcing, the very idea. The construction of S4 models and ZF. The axion of constructability is independent. Independence of the continuum hypothesis. Independence of the axiom of choice. Constructing classical models. Forcing background. References. Subject Index. Notation Index

Erscheint lt. Verlag	1.8.1996
Co-Autor	Melvin Fitting
Zusatzinfo	2 line figures, bibliography
Verlagsort	Oxford
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-19-852395-5 / 0198523955
ISBN-13	978-0-19-852395-6 / 9780198523956
Zustand	Neuware