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Kuratowski's free set theorem, named after Kazimierz Kuratowski, is a result of set theory, an area of mathematics. It is a result which has been largely forgotten for almost 50 years, but has been applied recently in solving several lattice theory problems, such as the congruence lattice problem .
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.
It develops some basic model theory (rather specifically aimed at models of set theory) and the theory of Gödel's constructible universe L. The book then proceeds to describe the method of forcing. Kunen completely rewrote the book for the 2011 edition (under the title "Set Theory"), including more model theory.
Download as PDF; Printable version; In other projects Wikidata item; ... This page is a list of articles related to set theory. Articles on individual set theory topics
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikimedia Commons; ... Pages in category "Basic concepts in set theory"
The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. However, the discovery of paradoxes in naive set theory, such as Russell's paradox, led to the desire for a more rigorous form of set theory that was free of these paradoxes. In 1908, Ernst Zermelo proposed the first axiomatic set theory, Zermelo set ...
Naive set theory is the original set theory developed by mathematicians at the end of the 19th century, treating sets simply as collections of things. Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's paradox ) in naive set theory.
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.