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*Mathematics | Program Guide: Set Theory
A guide to online Mathematics research for APUS faculty and students.
Lectures in Logic and Set Theory: Vol. 1 : Mathematical Logic by George J. TourlakisThis work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume I includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.
ISBN: 9780521753739
Publication Date: 2003-01-09
Lectures in Logic and Set Theory: Volume 2 : Set Theory by George J. TourlakisThis work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.
ISBN: 9780521753746
Publication Date: 2003-02-13
Set Theory and Its Logic by W. V. QuineThis is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
ISBN: 9780674802070
Publication Date: 1969-01-01
Set Theory and Its Philosophy by Michael PotterMichael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true.Set Theory and its Philosophyis a key text for philosophy, mathematical logic, and computer science.
ISBN: 9780199269730
Publication Date: 2004-03-11
Set Theory: Boolean-valued Models and Independence Proofs by John L. BellAimed at research students and academics in mathematics, mathematical logic, philosophy, and computer science, the text has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory, and includes recent developments in the field. Numerous exercises, along with the enlarged and entirely updated background material, make this an ideal text for students in logic and set theory.