Acoustic κ-density fluctuation waves in suprathermal κ function fluids

SMALL u κ AND LARGE 2 κ FOR SUPERCOMPACT κ

Garti and Shelah [2] state that one can force uκ to be κ+ for supercompact κ with 2κ arbitrarily large, using the technique of Džamonja and Shelah [1]. Here we spell out how this can be done. §

Compactification of κ-Frames

Cardinal characteristics at κ in a small u(κ) model

We provide a model where u(κ) < 2κ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that...

- 1 6 Not Collapsing Cardinals ≤ Κ in ( < Κ ) – Support Iterations

We deal with the problem of preserving various versions of completeness in (< κ)–support iterations of forcing notions, generalizing the case " S–complete proper is preserved by CS iterations for a stationary co-stationary S ⊆ ω 1 ". We give applications to Uniformization and the Whitehead problem. In particular, for a strongly inaccessible cardinal κ and a stationary set S ⊆ κ with fat complem...

Every (λ, Κ)-regular Ultrafilter Is (λ, Κ)-regular

We prove the following: Theorem A. If D is a (λ+, κ)-regular ultrafilter, then either (a) D is (λ, κ)-regular, or (b) the cofinality of the linear order ∏ D〈λ, <〉 is cf κ, and D is (λ, κ′)-regular for all κ′ < κ. Corollary B. Suppose that κ is singular, κ > λ and either λ is regular, or cf κ < cf λ. Then every (λ+n, κ)-regular ultrafilter is (λ, κ)-regular. We also discuss some consequences and...