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regular ultrafilter

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  • Partition regular — In mathematics, the notion of partition regularity in combinatorics is one approach to explaining when a set system is quite large.Given a set X, a collection of subsets mathbb{S} subset mathcal{P}(X) is called partition regular if for any A in… …   Wikipedia

  • Tychonoff's theorem — For other theorems named after Tychonoff, see Tychonoff s theorem (disambiguation). In mathematics, Tychonoff s theorem states that the product of any collection of compact topological spaces is compact. The theorem is named after Andrey… …   Wikipedia

  • PCF theory — is the name of a mathematical theory, introduced by Saharon Shelah (1978), that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on the cardinalities of power sets of singular cardinals, and has… …   Wikipedia

  • Boolean-valued model — In mathematical logic, a Boolean valued model is a generalization of the ordinary Tarskian notion of structure or model, in which the truth values of propositions are not limited to true and false , but take values in some fixed complete Boolean… …   Wikipedia

  • Stone–Čech compactification — In the mathematical discipline of general topology, Stone–Čech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space beta; X . The Stone–Čech compactification beta; X of a… …   Wikipedia

  • Forcing (mathematics) — For the use of forcing in recursion theory, see Forcing (recursion theory). In the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963,… …   Wikipedia

  • Measurable cardinal — In mathematics, a measurable cardinal is a certain kind of large cardinal number. Contents 1 Measurable 2 Real valued measurable 3 See also 4 References …   Wikipedia

  • metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …   Universalium

  • List of forcing notions — In mathematics, forcing is a method of constructing new models M[G] of set theory by adding a generic subset G of a poset P to a model M. The poset P used will determine what statements hold in the new universe (the extension ); to force a… …   Wikipedia

  • Cofinite — In mathematics, a cofinite subset of a set X is a subset Y whose complement in X is a finite set. In other words, Y contains all but finitely many elements of X . If the complement is not finite, but it is countable, then one says the set is… …   Wikipedia

  • Counterexamples in Topology —   Author(s) Lynn Arthur Steen J. Ar …   Wikipedia

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