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Intuitionistic Logic, Pointless Topology, and other Curiosities

by

Kimmo Rosenthal
Union College

January 11, 2010
4:30 pm
Bailey Hall 207

Refreshments will be served at 4:15 in Bailey 204


Abstract:

Intuitionistic logic is a system of logic where, contrary to the usual classical logic that students learn, the “law of excluded middle” does not hold. This means that it is not necessarily the case that for a statement A, either A is true or “not A” is true. If X is a set then P(X), the power set of X, is a nice algebraic model for the operations of classical logic. In the subject of topology, a topological space consists of a set X together with a designation of the open sets of X, O(X), subject to certain axioms. O(X) turns out to be a complete Heyting algebra (also known as locale, frame), which is a nice algebraic model for intuitionistic logic. We will provide a brief introduction to the subject of topology emphasizing this connection. We will discuss how one can often recover the points of a space, that is the elements of the set X, only knowing the algebraic structure of the opens (this is the pointless part of the talk) and we will briefly touch on other areas where this logic arises, hopefully showing that it is in fact more than a curiosity.


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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