Woodin cardinal
Woodin cardinal In set theory, a Woodin cardinal is a cardinal number κ such that for all ...
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Hyper-Woodin cardinal
Hyper-Woodin cardinal In axiomatic set theory, a hyper-Woodin cardinal is a kind of large cardinal. A cardinal κ is called hyper- ...
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Weakly hyper-Woodin cardinal
Weakly hyper-Woodin cardinal In axiomatic set theory, weakly hyper-Woodin cardinals are a kind of large cardinals. A cardinal κ is called weakly hyper-Woodin iff for every set S there ...
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Strong cardinal
Strong cardinal In mathematical set theory, a strong cardinal or λ-strong cardinal is a type of large cardinal. Specifically, a λ-strong cardinal is a cardinal number κ such ...
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Strongly compact cardinal
Strongly compact cardinal In mathematical set theory, a strongly compact cardinal is a certain kind of large cardinal number; their existence can neither be proven ... the standard axioms of set theory. A cardinal κ is strongly compact iff every κ ... many operands. The logic on a regular cardinal κ is defined by requiring the ...
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List of large cardinal properties
List of large cardinal properties Main article: Large cardinal property This page is a list of ... with the given property. Existence of a cardinal number κ of a given type implies ... above that type, and for most listed cardinal descriptions φ of lesser consistency strength, V ... cardinals (for countable α) 0 # (not a cardinal, but proves the existence of transitive ...
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Talk:Large cardinal property
Talk:Large cardinal property It might be nice if the ... about say a weak compact or measurable cardinal, but nobody talkes about say ineffable cardinals ... of large cardinals or List of large cardinal properties. Just a thought; I don't ... to write a general article about large cardinal properties in the abstract). --Trovatore 03:36 ... thing, it should really be at large cardinal property ("largeness" is not a property ...
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Category:Large cardinals
... in this section of this category. * Large cardinal property A Almost Ramsey cardinal E Erdős cardinal Extendible cardinal H Huge cardinal Hyper-Woodin cardinal I Inaccessible cardinal ...
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List of mathematical logic topics
... number Aleph-null Aleph-one Beth number Cardinal number Hartogs number Cartesian product Class (set ... Intersection (set theory) L L(R) Large cardinal property Musical set theory Ordinal number Infinite ... theory Analytical hierarchy Large cardinals Almost Ramsey cardinal Erdős cardinal Extendible cardinal Huge cardinal Hyper-Woodin cardinal Inaccessible ...
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Determinacy
... and large cardinals. In general, stronger large cardinal axioms prove the determinacy of larger pointclasses ... of inner models of slightly weaker large cardinal axioms than those used to prove the ... follows from the existence of a measurable cardinal that every analytic game (also called a ... result follows: If there is a measurable cardinal, then every game in the first ω ... the difference hierarchy over Π 1 1 . Woodin cardinals If there is a Woodin ...
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