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Set Theory of a Different Kind
Musical set theory provides concepts for categorizing musical objects and describing their relationships.
Resources in Set Theory
Lectures in Logic and Set Theory: Vol. 1 : Mathematical Logic by This 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.
Publication Date: 2003-01-09
Lectures in Logic and Set Theory: Volume 2 : Set Theory by This 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.
Publication Date: 2003-02-13
Set Theory and Its Logic by This 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.
Publication Date: 1969-01-01
Set Theory and Its Philosophy by Michael 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.
Publication Date: 2004-03-11
Set Theory: Boolean-valued Models and Independence Proofs by Aimed 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.
Publication Date: 2005-07-28
A History of Set Theory
University of Saint Andrews, United Kingdom.
Discrete Mathematics: Logic - Tutorial Exercises
University of Wollongong, New South Wales, Australia
Introduction to Discrete Structures - Whats and Whys
By Dr. Shunichi Toida, retired Professor Emeritus, Old Dominion University.
Introduction to Set Theory
YouTube, 2011. This video introduces the basic vocabulary used in set theory.
Just Math Tutorials - Discrete Math
Professor of Math, Austin, Community College. This site is rated 5 Stars by APUS Faculty.
Logic & Set Theory Links
University of Tennessee.
Math is Fun - Set Theory
Aimed at K-12 grade, this site includes interactive tools.
Stanford Encyclopedia of Philosophy
Sets & Set Theory
Tutorials for Discrete Mathematics
School of Science and Technology, University of New England.
A four-set Venn diagram.