/
lectern.tv
Play15s30s1x0:00/--:--
DoneWatched
Expand
University of Oxford·Corey Switzer
1:09:50
0:00/1:09:50
Type below to lock the video timestamp, or press S to capture a slide.
Some Set Theory of Kaufmann Models
An in-depth seminar on the set-theoretic properties of Kaufmann models, exploring their significance in the theory of models of arithmetic and their connection to set-theoretic incompactness.
Abstract. A Kaufmann model is an -like, recursively saturated, rather classless model of PA. Such models were shown to exist by Kaufmann under the assumption that Diamond holds, and in ZFC by Shelah via an absoluteness argument involving strong logics. They are important in the theory of models of arithmetic notably because they show that many classic results about countable, recursively saturated models of arithmetic cannot be extended to uncountable models. They are also a particularly interesting example of set theoretic incompactness at aleph_1, similar to an Aronszajn tree.