Independence Results (from ZFC) in Recursion Theory

			   Marcia Groszek
			  Dartmouth College

There are several ways in which a question in computability theory can lead to
an independence result from ZFC.  

Classical recursion theory is after all the study of the real numbers, and some
of its results and techniques depend on the nature of the reals as a whole. 
For example, a construction that can be extended from a countable set of reals
to a larger countable set may be extendible to all the reals provided the
continuum hypothesis holds, but may not necessarily extend to all the reals if
the continuum hypothesis fails.  

Computability questions beyond classical recursion theory can have an
essentially set theoretic nature.  For example, questions about the degrees of
constructibility of reals are intrinsically questions about possibilities in
different models of ZFC.  

This talk takes a brief look at an open question exemplifying each of these two
categories.