Author | Cameron, Peter J. author |
---|---|

Title | Sets, Logic and Categories [electronic resource] / by Peter J. Cameron |

Imprint | London : Springer London : Imprint: Springer, 1998 |

Connect to | http://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