This introduction to modern set theory covers the aspects of its two main general areas: classical set theory including large cardinals, infinitary combinatorics, descriptive set theory; and independence proofs starting with Goedel's proof around 1938 followed by Cohen's proof in 1963, whereby Cohen's method of forcing probably had a greater ...
Professor Jech gives here a unified treatment of the various forcing methods used in set theory, and presents their important applications. Product forcing, iterated forcing and proper forcing have proved powerful tools when studying the foundations of mathematics, for instance in consistency proofs. The book is based on graduate courses though ...
Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and the consequences of the axiom of choice. Subjects include consistency and independence, permutation models, and examples and counterexamples of the axiom's use. Each chapter contains several problems and concludes with some historical ...
Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, "Introduction to Set Theory, Third Edition" covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates ...
Magnetic control of the properties and the flow of liquids is a challenging field for basic research and for applications. This book is meant to be both an introduction to, and a state-of-the-art review of, this topic. Written in the form of a set of lectures and tutorial reviews, the book addresses the synthesis and characterization of magnetic ...
The intention of this book is threefold: presenting and advancing German reporting on income distribution and poverty, looking at experiences with advanced reporting schemes in two other EU countries, and discussing concepts for comparable social monitoring in the European Union. The first group of papers elaborates on recent findings for Germany ...
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