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Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Different extensions of first-order logic"

How does one capture the properties that aren’t definable by first-order sentences or even theories? One way is to allow infinitary conjunctions of first-order sentences. Another is to expand the language that is being used. In this talk I will discuss the cases when these two extensions coincide, and sketch a proof by W. Craig and R.L. Vaught that a computably axiomatizable theory can be finitely axiomatized using additional predicates.