set theory

  1. the branch of pure mathematics that deals with the nature and relations of sets
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How To Use set theory In A Sentence

  • By operationalizing Godel and set theory, Badiou's rationalism makes no concessions at all to the worldly or to the empirical.
  • This faith in the indubitable certainty of mathematical proofs was sadly shaken around 1900 by the discovery of the antinomies or paradoxes of set theory.
  • Let T be a standard, first-order axiomatization of set theory. Skolem's Paradox
  • Yet a fourth response was embodied in Ernst Zermelo's 1908 axiomatization of set theory. Russell's Paradox
  • In his core criticism of set theory, however, the later Wittgenstein denies this, saying that the diagonal proof does not prove non-denumerability, for “[i] t means nothing to say: “Therefore the X numbers are not denumerable” (RFM II, §10). Wittgenstein's Philosophy of Mathematics
  • Among logicians and mathematicians he is in addition famous for his work on set theory, model theory and algebra, which includes results and developments such as the Banach-Tarski paradox, the theorem on the indefinability of truth (see section 2 below), the completeness and decidability of elementary algebra and geometry, and the notions of cardinal, ordinal, relation and cylindric algebras. Alfred Tarski
  • His mathematical work concentrates on set theory, where his concern is the nature of a set.
  • After generalized goal programming model is established, FGGP with fuzzy goal sets and fuzzy parameters are studied, the solving methods using fuzzy set theory for FGGP are provided.
  • And philosophy is not far from the main concerns of such mathematical fields as logic, set theory, category theory, computability, and even analysis and geometry.
  • As for the AC, Gödel exhibits a definable well-ordering, that is, a formula of set theory which defines, in L, a well-ordering of all of L. Kurt Gödel
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