The main notions of set theory -- including cardinals, ordinals, and transfinite induction -- are fundamental to all mathematics. This advanced undergraduate- and graduate-level text offers a thorough exploration that extends from the history of set theory and its paradoxes to connections with symbolic and mathematical logic. Advanced topics include relations and functions, equipollence, and more. 1971 edition.
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Relational databases have quickly come to be regarded as a natural and efficient way of organizing information. Duplicate data can be eliminated and powerful set-theoretic operations can be used to...
This book is designed to help anyone understand the basics of fuzzy sets, whether or not they have a mathematical background. The book first presents a basic grounding...
An understanding of logic is essential to computer science. This book provides a highly accessible account of the logical basis required for reasoning about computer programs and applying logic in...
Anyone seeking a readable and relatively brief guide to logic can do no better than this classic introduction. A treat for both the intellect and the imagination, it profiles the...
Pulling up the Ladder discusses how Wittgenstein's early philosophy became widely known largely through the efforts of Russell and other empirically-minded British philosophers, and to a lesser extent, the scientifically-oriented...
This helpful volume explains and proves Godel's theorem, which states that arithmetic cannot be reduced to any axiomatic system. Written simply and directly, this book is intended for the student...
These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field....
Volume II of Classical Recursion Theory describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical sets. The first...