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AuthorCameron, Peter J. author
TitleSets, Logic and Categories [electronic resource] / by Peter J. Cameron
ImprintLondon : Springer London : Imprint: Springer, 1998
Connect tohttp://dx.doi.org/10.1007/978-1-4471-0589-3
Descript X, 182 p. online resource

SUMMARY

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gรถdel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material


CONTENT

1. Naรฏve set theory -- 2. Ordinal numbers -- 3. Logic -- 4. First-order logic -- 5. Model theory -- 6. Axiomatic set theory -- 7. Categories -- 8. Where to from here? -- Solutions to selected exercises -- References


Mathematics Category theory (Mathematics) Homological algebra K-theory Mathematical logic Mathematics Mathematical Logic and Foundations Category Theory Homological Algebra K-Theory



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