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Provability, Computability and Reflection

Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics

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This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics

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Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.

Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics

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Mathematical logic --- Set theory --- 51 --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- 51 Mathematics --- Set theory.

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a wonderful new book . . . Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews

Set theory --- Philosophy. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Philosophy --- Logic, Symbolic and mathematical --- Mathematics