Displaying similar documents to “Some properties of cardinal functions, II”

Some Remarks on Tall Cardinals and Failures of GCH

Arthur W. Apter (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

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

Similarity:

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.

A generic theorem in cardinal function inequalities

Alejandro Ramírez-Páramo (2008)

Colloquium Mathematicae

Similarity:

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

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

Similarity:

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

Similarity:

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...

Indestructibility, strongness, and level by level equivalence

Arthur W. Apter (2003)

Fundamenta Mathematicae

Similarity:

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.