# Category: Lemmas in set theory

Teichmüller–Tukey lemma
In mathematics, the Teichmüller–Tukey lemma (sometimes named just Tukey's lemma), named after John Tukey and Oswald Teichmüller, is a lemma that states that every nonempty collection of finite charact
Condensation lemma
In set theory, a branch of mathematics, the condensation lemma is a result about sets in theconstructible universe. It states that if X is a transitive set and is an elementary submodel of some level
Fodor's lemma
In mathematics, particularly in set theory, Fodor's lemma states the following: If is a regular, uncountable cardinal, is a stationary subset of , and is regressive (that is, for any , ) then there is
Rasiowa–Sikorski lemma
In axiomatic set theory, the Rasiowa–Sikorski lemma (named after Helena Rasiowa and Roman Sikorski) is one of the most fundamental facts used in the technique of forcing. In the area of forcing, a sub
Moschovakis coding lemma
The Moschovakis coding lemma is a lemma from descriptive set theory involving sets of real numbers under the axiom of determinacy (the principle — incompatible with choice — that every two-player inte
Fixed-point lemma for normal functions
The fixed-point lemma for normal functions is a basic result in axiomatic set theory stating that any normal function has arbitrarily large fixed points (Levy 1979: p. 117). It was first proved by Osw
Zorn's lemma
Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory. It states that a partially ordered set containing upper bounds for every chain (that is, every totally ordered su
Mostowski collapse lemma
In mathematical logic, the Mostowski collapse lemma, also known as the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by Andrzej Mostowski and.