20,527 research outputs found
Measurable cardinals and the cardinality of Lindel\"of spaces
If it is consistent that there is a measurable cardinal, then it is
consistent that all points g-delta Rothberger spaces have "small" cardinality.Comment: 9 pag
Rothberger gaps in fragmented ideals
The~\emph{Rothberger number} of a definable
ideal on is the least cardinal such that there
exists a Rothberger gap of type in the quotient algebra
. We investigate for a subclass of the ideals, the fragmented ideals,
and prove that for some of these ideals, like the linear growth ideal, the
Rothberger number is while for others, like the polynomial growth
ideal, it is above the additivity of measure. We also show that it is
consistent that there are infinitely many (even continuum many) different
Rothberger numbers associated with fragmented ideals.Comment: 28 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
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