16 papers
Power in Card with two Woodin cardinals
Farmer Schlutzenberg
Väänänen and Welch asked in the paper "When cardinals determine the power set: inner models and Härtig quantifier logic" which large cardinals are consistent with the power set…
Low level definability above large cardinals
Farmer Schlutzenberg
We study connections between definability in generalized descriptive set theory and large cardinals, under ZFC. We show that if is a limit of measurables then there is no well…
-translation for Varsovian models
Farmer Schlutzenberg
The technique of -translation is important in arguments calibrating the strengths of determinacy theories against large cardinals, for example in [9] and [1] in the paper's…
The initial segment condition for -supercompactness
Farmer Schlutzenberg
We give a development of the fine structure of mice with long extenders, to the level of -supercompact cardinals . We do this using a hierarchy with features more analogo…
Full normalization for -supercompactness
Farmer Schlutzenberg
We extend the normalization results of the author's paper "Full normalization for transfinite stacks" [5] to mice at the level of -supercompactness: given a normal iteration…
Fine structure from normal iterability
Farmer Schlutzenberg
We show that (i) the standard fine structural properties for premice follow from normal iterability (whereas the classical proof relies on iterability for stacks of normal trees),…