23 research outputs found
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
More Results on Regular Ultrafilters in ZFC
We prove, in ZFC alone, some new results on regularity and decomposability of
ultrafilters.
We also list some problems, and furnish applications to topological spaces
and to extended logics.Comment: 57 page
Compactness of powers of \omega
We characterize exactly the compactness properties of the product of \kappa\
copies of the space \omega\ with the discrete topology. The characterization
involves uniform ultrafilters, infinitary languages, and the existence of
nonstandard elements in elementary estensions. We also have results involving
products of possibly uncountable regular cardinals.Comment: v2 slightly improve