Set Theory
The mathematical theory of Sets. Set theory is closely associated with the branch of mathematics known asLogic.
There are a number of different versions of set theory, each with its own rules and Axioms. In order ofincreasing Consistency Strength, several versions of set theory include Peano Arithmetic (ordinaryAlgebra), second-order arithmetic (Analysis), Zermelo-Fraenkel Set Theory, Mahlo, weakly compact,hyper-Mahlo, ineffable, measurable, Ramsey, supercompact, huge, and 
-huge set theory.
Given a set of Real Numbers, there are 14 versions of set theory which can be obtained using onlyclosure and complement (Beeler et al. 1972, Item 105).
See also Axiomatic Set Theory, Consistency Strength, Continuum Hypothesis, Descriptive Set Theory,Impredicative, Naive Set Theory, Peano Arithmetic, Set, Zermelo-Fraenkel Set Theory
References
Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, pp. 36-44, Feb. 1972. Brown, K. S. ``Set Theory and Foundations.''http://www.seanet.com/~ksbrown/ifoundat.htm. Courant, R. and Robbins, H. ``The Algebra of Sets.'' Supplement to Ch. 2 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 108-116, 1996. Devlin, K. The Joy of Sets: Fundamentals of Contemporary Set Theory, 2nd ed. New York: Springer-Verlag, 1993. Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974. MacTutor History of Mathematics Archive. ``The Beginnings of Set Theory.'' http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Beginnings_of_set_theory.html. Stewart, I. The Problems of Mathematics, 2nd ed. Oxford: Oxford University Press, p. 96, 1987.
Set Theory
- Smith Number
- Smith's Markov Process Theorem
- Smith's Network Theorem
- Smooth Manifold
- Smooth Number
- Smooth Surface
- Snake
- Snake Eyes
- Snake Oil Method
- Snake Polyiamond
- Snedecor's F-Distribution
- Snellius-Pothenot Problem
- Snowflake
- Snub Cube
- Snub Cuboctahedron
- Snub Disphenoid
- Snub Dodecadodecahedron
- Snub Dodecahedron
- Snub Icosidodecadodecahedron
- Snub Icosidodecahedron
- Snub Polyhedron
- Snub Square Antiprism
- Soap Bubble
- Soccer Ball
- Sociable Numbers