Proof, Sets, and Logic
by M. Randall Holmes
Publisher: Boise State University 2009
Number of pages: 207
This textbook is intended to communicate something about proof, sets, and logic. It is about the foundations of mathematics, a subject which results when mathematicians examine the subject matter and the practice of their own subject very carefully.
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by Gary Hardegree - UMass Amherst
From the table of contents: Basic material on set theory - Overview / Summary, Basic Concepts, Relations, Functions, Natural Numbers, Cardinal Numbers; Rules for Derivations; Formal Languages; Mathematical Induction; Brief History of Numeration.
by David Marker - University of Illinois at Chicago
These are informal notes for a course in Descriptive Set Theory. While I hope to give a fairly broad survey of the subject we will be concentrating on problems about group actions, particularly those motivated by Vaught's conjecture.
by Thoralf A. Skolem - University of Notre Dame
The book contains a series of lectures on abstract set theory given at the University of Notre Dame. After some historical remarks the chief ideas of the naive set theory are explained. Then the axiomatic theory of Zermelo-Fraenkel is developed.
by A. C. Walczak-Typke
From the table of contents: Learning to Speak; The Axioms of Set Theory; Orders and Ordinals; Cardinal Numbers; The Axiom of Regularity; Some Consistency Results; Goedel's Constructible Universe L; Independence of AC from ZFU; Forcing.