323 research outputs found
Menger's covering property and groupwise density
We establish a surprising connection between Menger's classical covering
property and Blass's modern combinatorial notion of groupwise density. This
connection implies a short proof of the groupwise density bound on the
additivity number for Menger's property.Comment: Small update
A semifilter approach to selection principles
We develop the semifilter approach to the classical Menger and Hurewicz
covering properties and show that the small cardinal g is a lower bound of the
additivity number of the family of Menger subspaces of the Baire space, and
under u< g every subset X of the real line with the property
Split(Lambda,Lambda) is Hurewicz.Comment: LaTeX 2e, 15 pages, submitted to Comment. Math. Univ. Carolina
Covering the Baire space by families which are not finitely dominating
It is consistent (relative to ZFC) that the union of max{b,g} many families
in the Baire space which are not finitely dominating is not dominating. In
particular, it is consistent that for each nonprincipal ultrafilter U, the
cofinality of the reduced ultrapower w^w/U is greater than max{b,g}. The model
is constructed by oracle chain condition forcing, to which we give a
self-contained introduction.Comment: Small update
Template iterations with non-definable ccc forcing notions
We present a version with non-definable forcing notions of Shelah's theory of
iterated forcing along a template. Our main result, as an application, is that,
if is a measurable cardinal and are
uncountable regular cardinals, then there is a ccc poset forcing
. Another
application is to get models with large continuum where the groupwise-density
number assumes an arbitrary regular value.Comment: To appear in the Annals of Pure and Applied Logic, 45 pages, 2
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