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Math Logic Seminars
Schedule for Fall 2009 Visit http://logic.cmu.edu/seminar/seminar.html for seminar details.TUESDAY, October 6, 2009William Boney, Carnegie Mellon University Model theory of L_{omega_1, omega} ABSTRACT: L_{omega_1, omega} is the language we get when we start with L and allow for countable conjunctions and disjunctions. Among other things, this allows us to talk about things involving finiteness and countability and allows us to omit countable types with a sentence. However, we lose the Compactness Theorem and the Upward Lowenheim-Skolem-Tarski Theorem, our two favorite methods for constructing models. In this talk, we introduce L_{omega_1, omega} and some of the model construction methods that aim to replace these. Time: 12:00 P.M. TUESDAY, November 3, 2009Peter Lumsdaine, Carnegie Mellon University Fixed-point theorems, constructively ABSTRACT: The Bourbaki-Witt and Tarski fixed-point theorems for chain-complete posets are two minor gems of early set theory: simple and natural statements about posets, easily and elegantly proven with transfinite induction. In constructive logic, the situation is less simple. I will sketch a counterexample (in the effective topos, a realisability model) showing that neither can be proven entirely constructively; and I will show how they are in fact equivalent to the existence of enough ordinals. Time: 12:00 P.M. |
