552 research outputs found
Generic Large Cardinals and Systems of Filters
We introduce the notion of -system of filters, generalizing the
standard definitions of both extenders and towers of normal ideals. This
provides a framework to develop the theory of extenders and towers in a more
general and concise way. In this framework we investigate the topic of
definability of generic large cardinals properties.Comment: 36 page
Unreachability of Inductive-Like Pointclasses in
Hjorth proved from that there is no sequence of distinct
sets of length . Sargsyan extended Hjorth's technique
to show there is no sequence of distinct sets of length
. Sargsyan conjectured an analogous property is true for any
regular Suslin pointclass in -- i.e. if is a regular Suslin
cardinal in , then there is no sequence of distinct -Suslin sets
of length in . We prove this in the case that the pointclass
is inductive-like
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