Speaker: Harvey Friedman
Title: Issues in the Foundations of Mathematics

The lecture will discuss my efforts over the past 35 years concerning three
crucial issues in the foundations of mathematics that are deeply connected
with the great seminal work and writings of Kurt Godel.

1. To what extent can set theoretic methods, including the so called large
cardinal axioms, be used in an essential way to further the development of
normal mathematics?

2. Are there fundamental principles of a general philosophical nature which
can be used to give consistency proofs of set theory, including the so
called large cardinal axioms?

3. To what extent, and in what sense, is the natural hierarchy of logical
strengths represented by familiar systems ranging from exponential function
arithmetic to ZF + j:V into V robust?

In connection with 1, we will discuss Boolean relation theory and the
criterion of "beauty". In connection with 2, we will discuss the two mind
interpretation of predication. In connection with 3, we will discuss the
new primitive independence results from ZFC.

Work Address: Department of Mathematics
	The Ohio State University
	Roomm 220, Mathematics Building
	231 West 18th Avenue
	Columbus, OH 43210

Electronic Mail: friedman@math.ohio-state.edu