Between Ramsey and measurable cardinals
arxiv(2023)
摘要
We study several intertwined hierarchies between $\kappa$-Ramsey cardinals
and measurable cardinals to illuminate the structure of the large cardinal
hierarchy in this region. In particular, we study baby versions of
measurability introduced by Bovykin and McKenzie and some variants by locating
these notions in the large cardinal hierarchy and providing characterisations
via filter games. As an application, we determine the theory of the universe up
to a measurable cardinal.
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