Speaker:
Jim Helmreich
Title:
Tarski's High School Identities
Abstract:
Using the standard axioms for multiplication and addition on the natural numbers (distributive, associative, commutative etc.), one can derive all other identities true of the natural numbers. Now suppose one adds to the standard axioms ones for exponentiation. Call this set of axioms the High School Identities. Alfred Tarski asked whether the same thing were true: are all statements involving addition, multiplication and exponentiation that are true of the natural numbers derivable from the HSIs? A "no" answer to this question suggests the interesting possibility of nonstandard models for the HSIs. I will discuss some of the history and work accomplished on this problem.
Audience:
This talk should be accessible to a general audience, including those who are not mathematics majors.
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