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The Method of Universal Instances

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If you have a question about this talk, please contact Mary Fortune.

Part of the TCSS Symposium

Suppose you want to check some propositions P_1, P_2, P_3, ... about a class C of mathematical objects. In this situation, a universal instance is an object A in the class C such that, for each n, P_n is true for A if and only if P_n is true for every object in the class C. Universal instances do not exist in general, but sometimes we can find exceptionally nice universal instances where it becomes much easier to check the propositions of interest. I will give some simple examples of this phenomenon, and time permitting, I may discuss general results.

This talk is part of the Trinity Mathematical Society series.

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