Search results
Results from the WOW.Com Content Network
Set Theory: An Introduction to Independence Proofs is a textbook and reference work in set theory by Kenneth Kunen. It starts from basic notions, including the ZFC axioms, and quickly develops combinatorial notions such as trees, Suslin's problem, , and Martin's axiom. It develops some basic model theory (rather specifically aimed at models of ...
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...
Paul Halmos. Publication date. 1960. See also Naive set theory for the mathematical topic. Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. [1] Originally published by Van Nostrand in 1960, [2] it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974.
It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.
Class (set theory) In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like collections while differing from sets so as to avoid paradoxes, especially ...
Grundzüge der Mengenlehre (German for "Basics of Set Theory") is a book on set theory written by Felix Hausdorff. First published in April 1914, Grundzüge der Mengenlehre was the first comprehensive introduction to set theory. In addition to the systematic treatment of known results in set theory, the book also contains chapters on measure ...
A naive theory in the sense of "naive set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and operations on sets. Such theory treats sets as platonic absolute objects. The words and, or, if ... then, not, for some, for every are treated as in ordinary mathematics.
Morse–Kelley set theory is named after mathematicians John L. Kelley and Anthony Morse and was first set out by Wang (1949) and later in an appendix to Kelley's textbook General Topology (1955), a graduate level introduction to topology. Kelley said the system in his book was a variant of the systems due to Thoralf Skolem and Morse.