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Graduate Seminar
Paul McKenney Carnegie Mellon University Title: Pathology and rigidity in set theory Abstract: Cantor proved long ago that every countable, dense linear order, without endpoints, is orderisomorphic to the rational numbers with their usual order. One might ask whether a similar theorem holds for the uncountable linear orders. Assuming the continuum hypothesis, the answer is no, and in fact the number of isomorphism types in this case is unfathomably large. But an alternate axiom, called the proper forcing axiom, turns out to answer this and many other questions in a satisfying way. Moreover, it has interesting combinatorial consequences that can be stated without any settheoretic language whatsoever. I'll talk about all this with an eye towards what's true in the "real world." Date: Thursday, April 4, 2013 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Brian Kell 