CONFERENCE: AMS-IMS-SIAM Summer Research Conference
	    ``Computability Theory and Applications''
	      Boulder, Colorado, June 13-17, 1999
 
	  DATE AND TIME: Wednesday, June 16, 1:30-2:15 PM
 
     SPEAKER: Stephen G. Simpson, Pennsylvania State University
 
TITLE: Foundations of mathematics, and open problems in reverse mathematics
 
ABSTRACT:
 
In the first part of the talk, I will give a broad overview of some
issues and programs in foundations of mathematics, including:
 
   selection of basic concepts
   selection of axioms
   the hierarchy of consistency strengths
   the need for new axioms
   practical completeness
   reverse mathematics
 
In the second part of the talk, I will mention some open problems
arising from known results in reverse mathematics, including:
 
   reverse mathematics for analysis (Tietze extension theorem, etc)
   reverse mathematics for functional analysis (Krein/Shmulian, etc)
   reverse mathematics for Ramsey theory (Hindman, Szemeredi, Carlson)
   strength of statements in WQO theory (trees with gap condition)
   reverse mathematics for BQO theory (Nash-Williams, Laver)
   weakening the base theory by dropping Sigma01 induction