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Result in mathematics and set theory
logic, the Mostowski collapse lemma, also known as the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by Andrzej Mostowski (1949, theorem
Mostowski_collapse_lemma
Polish mathematician (1913–1975)
foundations of mathematics and is perhaps best remembered for the Mostowski collapse lemma. He was a member of the Polish Academy of Sciences and a representative
Andrzej_Mostowski
Surname list
Warsaw Andrzej Mostowski (1913 - 1975), a Polish mathematician Mostowski collapse lemma, in mathematical logic Ehrenfeucht–Mostowski theorem, in model
Mostowski
lemma Mostowski collapse lemma Teichmüller–Tukey lemma also known as Tukey's lemma Zorn's lemma; equivalent to the axiom of choice Covering lemma Delta
List_of_lemmas
Generalization of "n-th" to infinite cases
membership. This mapping is known as the Mostowski collapse lemma. When applied to a well-ordering, the Mostowski collapse yields a specific set S {\displaystyle
Ordinal_number
Set theory concept
M. The restriction to transitive models is not serious, as the Mostowski collapse lemma implies that every "reasonable" (well-founded, extensional) model
Boolean-valued_model
Substructure of a set theoretical universe
In fact, the downward Löwenheim–Skolem theorem together with Mostowski collapse lemma can convert any standard (set) model of ZFC into a standard transitive
Standard_model_(set_theory)
Technique for proving independence results
transitive model can be obtained from any standard model through the Mostowski collapse lemma, but the existence of any standard model of Z F C {\displaystyle
Forcing_(mathematics)
System of mathematical set theory
fails to prove some common theorems in set theory, such as the Mostowski collapse lemma. Constructible universe Admissible ordinal Hereditarily countable
Kripke–Platek_set_theory
Axiom of set theory
clarification of what one means by “set”, as elaborated on by the Mostowski collapse lemma (which provides the converse: that not only is membership on every
Axiom_of_regularity
Type of binary relation
the chain ω, n − 1, n − 2, ..., 2, 1 has length n for any n. The Mostowski collapse lemma implies that set membership is a universal among the extensional
Well-founded_relation
Month of 1913
clubs in the country. Born: Andrzej Mostowski, Polish mathematician, developed the set theory Mostowski collapse lemma; in Lemberg, Austria-Hungary (present-day
November_1913
Proof that every structure with certain properties is isomorphic to another structure
embedded) subcategory of a category of modules over some ring. Mostowski's collapsing theorem states that every well-founded extensional structure is
Representation_theorem
Morse–Kelley set theory, a set theory with classes Mostowski 1. Andrzej Mostowski 2. The Mostowski collapse is a transitive class associated to a well founded
Glossary_of_set_theory
Particular class of sets which can be described entirely in terms of simpler sets
{\displaystyle L_{\beta }} . By the downward Löwenheim–Skolem theorem and Mostowski collapse, there must be some transitive set K {\displaystyle K} containing
Constructible_universe
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MOSTOWSKI COLLAPSE-LEMMA
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