10 research outputs found
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
The Largest Suslin Axiom
We develop the basic fine structure theory of the minimal model of the
Largest Suslin Axiom. In particular, we prove that that the minimal model of
the Largest Suslin Axiom satisfies the Mouse Set Conjecture, and that the
Proper Forcing Axiom implies the minimal model of the Largest Suslin Axiom
exists
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Set Theory
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