Suppose there is a fully nonregular ultrafilter U on ω2. Then: (1) There is an inner model with a cardinal κ of Mitchell order κ+. In particular, if ...

We obtain lower bounds for the consistency strength of fully nonregular ultrafilters on ω2. Type: Research Article. Information.

We obtain lower bounds for the consistency strength of fully nonregular ultrafilters on ω2. Citation. Download Citation. Sean Cox. "Nonregular ultrafilters on ω ...

The relationship between the existence of nonregular ultrafilters and large cardinals in the constructible universe is studied.

For a free ultrafilter U on ω we study several cardinal characteristics which describe part of the combinatorial structure of U. We provide various ...

Suppose h e M, h witnesses ο+(ω^ω) in Μ and for all ρ € (ω^ω)Μ the set. [a <o>f | ρ € Λ(α)} is stationary within M. Then there is an iteration.

Mar 11, 2019 · We say an ultrafilter Z on ω is Tensor-representable if there are non-Keisler-Rudin-equivalent ultrafilters U,V and a bijection ψ:ω2→ω such that ...

These are the free (“non-principal”) ultrafilters with bases that are totally ordered by the order ⊂∗ of almost inclusion. It is ZFC-independent whether simple ...

Nonregular ultrafilters on ω2.Sean Cox - 2011 - Journal of Symbolic Logic 76 (3):827-845. Narrow coverings of ω-ary product spaces.Randall Dougherty - 1997 ...

In particular, if an ultrafilter U on ω1 has the property that |ω1 ω/U| = ω1, then U must be nonregular. Nonregularity is a weakening of countable completeness.