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Sets, Groups and Knots
by Curtis T. McMullen - Harvard University , 2008
Introduction to conceptual and axiomatic mathematics, the writing of proofs, mathematical culture, with sets, groups and knots as topics. From the table of contents: Introduction; Set Theory; Group Theory; Knot Theory; Summary.
Descriptive Set Theory
by David Marker - University of Illinois at Chicago , 2002
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.
Axiomatic Set Theory
by Michael Meyling , 2011
This document contains the mathematical foundation of set theory. Goal is the presentation of elementary results which are needed in other disciplines. Although the presentation is axiomatic the results shall match the mathematical usage.
Axiomatic Set Theory I
by A. C. Walczak-Typke , 2009
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.
Notes on Set Theory
by Michael Makkai - McGill University , 2000
Contents: Sets and classes; The universe of pure sets; Further principles of set-construction; Natural numbers and ordinals; Well-founded Relations and recursion; Indexing by ordinals and the axiom of choice; Well-orderings; Zorn's lema; etc.
Proof, Sets, and Logic
by M. Randall Holmes - Boise State University , 2009
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.
Elementary Set Theory with a Universal Set
by Randall Holmes , 2005
From the table of contents: The Set Concept; Boolean Operations on Sets; Building Finite Structures; The Theory of Relations; Sentences and Sets; Stratified Comprehension; Philosophical Interlude; Equivalence and Order; Introducing Functions; etc.
by Gary Hardegree - UMass Amherst , 2003
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.
Abstract Set Theory
by Thoralf A. Skolem - University of Notre Dame , 1962
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.
The Continuum and Other Types of Serial Order
by Edward V. Huntington - Dover Publications , 1917
This classic of mathematics presents the best systematic elementary account of the modern theory of the continuum as a type of serial order. Based on the Dedekind-Cantor ordinal theory, it requires no knowledge of higher mathematics.
Descriptive Set Theory
by Yiannis N. Moschovakis - American Mathematical Society , 2009
This monograph develops Descriptive Set Theory from its classical roots to the modern 'effective' theory. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results established since the 1980s.
An Introduction to Set Theory
by William A. R. Weiss - University of Toronto , 2008
These notes for a graduate course in set theory cover the axioms of set theory, the natural numbers, the ordinal numbers, relations and orderings, cardinality, the real numbers, the universe, reflection, elementary submodels, and constructibility.
Sets, Relations, Functions
by Ivo Düntsch, Günther Gediga - Methodos Publishers (UK) , 2000
Introduction to the set theoretic tools for anyone who comes into contact with modern Mathematics. The intended audience are students of any subject or practitioners who need some knowledge of set operations and related topics.