singular cardinal造句
造句與例句
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- K c computes the successors of measurable and many singular cardinals correctly.
- Proving the existence of singular cardinals requires the Fraenkel to postulate this axiom.
- Therefore only the aleph numbers can meaningfully be called regular or singular cardinals.
- The preceding examples both are singular cardinals of cofinality ? and hence they are not inaccessible.
- The negation of the singular cardinals hypothesis is intimately related to violating the GCH at a measurable cardinal.
- In particular, then, if \ kappa is the least counterexample to the singular cardinals hypothesis, then cf ( \ kappa ) = \ omega.
- The following important fact follows from Silver's theorem : if the singular cardinals hypothesis holds for all singular cardinals of countable cofinality, then it holds for all singular cardinals.
- The following important fact follows from Silver's theorem : if the singular cardinals hypothesis holds for all singular cardinals of countable cofinality, then it holds for all singular cardinals.
- The following important fact follows from Silver's theorem : if the singular cardinals hypothesis holds for all singular cardinals of countable cofinality, then it holds for all singular cardinals.
- In Easton's model the powersets of singular cardinals have the smallest possible cardinality compatible with the conditions that 2 ? has cofinality greater than ? and is a non-decreasing function of ?.
- It's difficult to see singular cardinal in a sentence. 用singular cardinal造句挺難的
- As I recall the singular cardinal hypothesis can be stated as gimel ( & kappa ) = & kappa; + for every singular & kappa; .-- Trovatore 19 : 37, 27 September 2006 ( UTC)
- In his 1975 paper " On the Singular Cardinals Problem ", Silver proved that if a consistent with ZFC . He introduced the notion of a " master condition ", which became an important tool in forcing proofs involving large cardinals.
- :: There is yet another form of this in use : searching for the plural Cardinals takes you directly to a disambiguation page for the singular Cardinal, which has links to articles involving both singular and plural forms of the word, but doesn't mention the plural forms at the top . talk ) 13 : 27, 13 January 2015 ( UTC)
- It is not known whether the Generalized Suslin Hypothesis is consistent with the Generalized Continuum Hypothesis; however, since the combination implies the negation of the square principle at a singular strong limit cardinal in fact, at all singular cardinals and all regular successor cardinals it implies that the axiom of determinacy holds in L ( R ) and is believed to imply the existence of an inner model with a superstrong cardinal.
- Other examples of his results in pure model theory include : generalizing the Keisler Shelah omitting types theorem for \ mathit { L ( Q ) } to successors of singular cardinals; with Shelah, introducing the notion of unsuper-stability for infinitary logics, and proving a nonstructure theorem, which is used to resolve a problem of Fuchs and Salce in the theory of modules; with Hart, proving a structure theorem for \ mathit { L } _ { \ omega _ 1, \ omega }, which resolves Morley's conjecture for excellent classes; and the notion of relative saturation and its connection to Shelah's conjecture for \ mathit { L } _ { \ omega _ 1, \ omega }.
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