Series: Penn State Logic Seminar

Date: Tuesday, September 9, 2003

Time: 2:30 - 3:45 PM

Place: 113 McAllister Building

Speaker: Stephen G. Simpson, Penn State, Mathematics

Title: Almost Everywhere Domination


This is joint work with Natasha Dobrinen.  Consider the usual "fair
coin" measure on the space C of infinite sequences of 0's and 1's.
Let us say that a Turing degree d is almost everywhere dominating if,
for almost all X in C, every function recursive in X is eventually
dominated by a function of degree d.  We present some partial results
on the problem of characterizing the Turing degrees which are almost
everywhere dominating.  We show how this problem is related to a
problem in the reverse mathematics of measure theory.  We also
consider some related notions and problems.