Displaying similar documents to “Cardinal arithmetic of general relational systems”

Some Remarks on Tall Cardinals and Failures of GCH

Arthur W. Apter (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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We investigate two global GCH patterns which are consistent with the existence of a tall cardinal, and also present some related open questions.

Some applications of Sargsyan's equiconsistency method

Arthur W. Apter (2012)

Fundamenta Mathematicae

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We apply techniques due to Sargsyan to reduce the consistency strength of the assumptions used to establish an indestructibility theorem for supercompactness. We then show how these and additional techniques due to Sargsyan may be employed to establish an equiconsistency for a related indestructibility theorem for strongness.

Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions

Arthur W. Apter (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal κ has its strong compactness indestructible under κ-directed closed forcing. This is in analogy to and generalizes the author's result in Arch. Math. Logic 46 (2007), but without the restriction that no cardinal is supercompact up to an inaccessible cardinal.

HOD-supercompactness, Indestructibility, and Level by Level Equivalence

Arthur W. Apter, Shoshana Friedman (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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In an attempt to extend the property of being supercompact but not HOD-supercompact to a proper class of indestructibly supercompact cardinals, a theorem is discovered about a proper class of indestructibly supercompact cardinals which reveals a surprising incompatibility. However, it is still possible to force to get a model in which the property of being supercompact but not HOD-supercompact holds for the least supercompact cardinal κ₀, κ₀ is indestructibly supercompact, the strongly...

A generic theorem in cardinal function inequalities

Alejandro Ramírez-Páramo (2008)

Colloquium Mathematicae

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We establish a general technical result, which provides an algorithm to prove cardinal inequalities and relative versions of cardinal inequalities.

Indestructibility, strongness, and level by level equivalence

Arthur W. Apter (2003)

Fundamenta Mathematicae

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We construct a model in which there is a strong cardinal κ whose strongness is indestructible under κ-strategically closed forcing and in which level by level equivalence between strong compactness and supercompactness holds non-trivially.

More Easton theorems for level by level equivalence

Arthur W. Apter (2012)

Colloquium Mathematicae

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We establish two new Easton theorems for the least supercompact cardinal that are consistent with the level by level equivalence between strong compactness and supercompactness. These theorems generalize Theorem 1 in our earlier paper [Math. Logic Quart. 51 (2005)]. In both our ground model and the model witnessing the conclusions of our present theorems, there are no restrictions on the structure of the class of supercompact cardinals.