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The Theory of Relations

by

Kimmo Rosenthal
Union College

October 24, 2011
5 pm
Bailey Hall 207

Refreshments will be served in Bailey Hall 204 at 4:45


Abstract:

Upon espying the title a student’s first reaction might be that this is a blurb for the next Dr. Phil show, or perhaps an invitation to a “group-hug” gathering sponsored by some campus office at a Minerva, however while this talk will be neither salacious, as in the first case, nor heart-warming, as in the second case, hopefully it will be interesting and accessible, even to students currently taking Math 199. We will take a close look at the set Rel(X), the relations on a set X, which has a very rich algebraic structure. Students encounter reflexive, symmetric and transitive relations, otherwise known as equivalence relations, in Math 199, but little time is spent on actually studying relations in general. They are somewhat like the neglected stepchild of Math 199, occasionally trotted out for the amusement of the visitors, but mostly consigned to an attic bedroom.

We will briefly discuss their history, populated by names such as de Morgan, Russell, and Tarski, and explore the various operations that can be performed on relations and their interrelationships. Time permitting we will take a look at how these operations and interrelationships appear in a variety of other contexts, including abstract algebra and logic, in the latter case more specifically in the context of (possibly non-commutative) linear logic, a “logic of resources”.


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