2,798 research outputs found
Spectra of Tukey types of ultrafilters on Boolean algebras
Extending recent investigations on the structure of Tukey types of
ultrafilters on to Boolean algebras in general, we
classify the spectra of Tukey types of ultrafilters for several classes of
Boolean algebras, including interval algebras, tree algebras, and pseudo-tree
algebras.Comment: 18 page
The ultrafilter number for singular cardinals
We prove the consistency of a singular cardinal with small value of
the ultrafilter number , and arbitrarily large value of .Comment: 8 page
A hierarchy of Ramsey-like cardinals
We introduce a hierarchy of large cardinals between weakly compact and
measurable cardinals, that is closely related to the Ramsey-like cardinals
introduced by Victoria Gitman, and is based on certain infinite filter games,
however also has a range of equivalent characterizations in terms of elementary
embeddings. The aim of this paper is to locate the Ramsey-like cardinals
studied by Gitman, and other well-known large cardinal notions, in this
hierarchy
Ultrafilter convergence in ordered topological spaces
We characterize ultrafilter convergence and ultrafilter compactness in
linearly ordered and generalized ordered topological spaces. In such spaces,
and for every ultrafilter , the notions of -compactness and of
-pseudocompactness are equivalent. Any product of initially
-compact generalized ordered topological spaces is still initially
-compact. On the other hand, preservation under products of certain
compactness properties are independent from the usual axioms for set theory.Comment: v. 2: some additions and some improvement
Forcing lightface definable well-orders without the CGH
For any given uncountable cardinal with , we present a forcing that is -directed closed, has the -c.c. and introduces a lightface definable well-order of . We use this to define a global iteration that does this for all such simultaneously and is capable of preserving the existence of many large cardinals in the universe
- …