Results 81 to 90 of about 199 (115)

Small measurable cardinals. [PDF]

Arch Math Log
Hayut Y, Karagila A.
europepmc   +1 more source

More minimal non- σ -scattered linear orders. [PDF]

Eur J Math
Shalev R.
europepmc   +1 more source

The enhanced Levinski property and the class of supercompact cardinals

The enhanced Levinski property and the class of supercompact cardinals
We define a generalization of a property originally due to Levinski [13], show its relative consistency, and investigate some of its possible interactions with the class of supercompact cardinals.
openaire  

The Tree Property

. We construct a model in which there are no @n-Aronszajn trees for any finite n 2, starting from a model with infinitely many supercompact cardinals.
Matthew Foreman, James Cummings
core  

Maximality Principle under a Laver-generic supercompact cardinal (New Developments in Forcing and Cardinal Arithmetic)

Maximality Principle under a Laver-generic supercompact cardinal (New Developments in Forcing and Cardinal Arithmetic)
We give a survey on the set-theoretic axioms formulated in terms of existence of a Laver-generic large cardinal. We show that the Maximality Principle without parameters is independentover ZFC with the axiom asserting the existence of a P-Laver generically supercompact cardinal for an iterable class of posets P as far as the existence of such a ...
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Generically supercompact cardinals by forcing with chain conditions (Recent Developments in Set Theory of the Reals)

Generically supercompact cardinals by forcing with chain conditions (Recent Developments in Set Theory of the Reals)
A ccc-generically supercompact cardinal κ, can be smaller than or equal to the continuum. On the other hand, such a cardinal κ, still satisfies diverse largeness properties, like that it is a stationary limit of ccc-generically measurable cardinals (Theorem 4.1).
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SUPERCOMPACT CARDINALS IN ZF (Recent Developments in Axiomatic Set Theory)

SUPERCOMPACT CARDINALS IN ZF (Recent Developments in Axiomatic Set Theory)
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SMALL $mathfrak{u}_kappa$ AND LARGE $2^kappa$ FOR SUPERCOMPACT $kappa$ (Forcing extensions and large cardinals)

SMALL $mathfrak{u}_kappa$ AND LARGE $2^kappa$ FOR SUPERCOMPACT $kappa$ (Forcing extensions and large cardinals)
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On the role of supercompact and extendible cardinals in logic

Israel Journal of Mathematics, 1971
It is proved that the existence of supercompact cardinal is equivalent to a certain Skolem-Lowenheim Theorem for second order logic, whereas the existence of extendible cardinal is equivalent to a certain compactness theorem for that logic. It is also proved that a certain axiom schema related to model theory implies the existence of many extendible ...
exaly   +2 more sources