6,356 research outputs found
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
Combinatorial Properties and Dependent choice in symmetric extensions based on L\'{e}vy Collapse
We work with symmetric extensions based on L\'{e}vy Collapse and extend a few
results of Arthur Apter. We prove a conjecture of Ioanna Dimitriou from her
P.h.d. thesis. We also observe that if is a model of ZFC, then
can be preserved in the symmetric extension of in terms of
symmetric system , if
is -distributive and is -complete.
Further we observe that if is a model of ZF + , then
can be preserved in the symmetric extension of in terms of
symmetric system , if
is -strategically closed and is
-complete.Comment: Revised versio
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