3,700 research outputs found
Dense ideals and cardinal arithmetic
From large cardinals we show the consistency of normal, fine,
-complete -dense ideals on for
successor . We explore the interplay between dense ideals, cardinal
arithmetic, and squares, answering some open questions of Foreman
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
Recommended from our members
Mini-Workshop: Feinstrukturtheorie und Innere Modelle
This workshop presented recent advances in fine structure and inner model theory. There were extended tutorials on hod mice and the Mouse Set Conjecture, suitable extender sequences and their fine structure, and the construction of true K below a Woodin cardinal in ZFC. The remaining talks involved precipitous ideals, stationary set reflection, failure of SCH in ZF, nonthreadable square sequences, reverse mathematics, forcing axioms, covering properties of canonical inner models, and “set theoretic geology.
- …