🚀 go-pugleaf

                     UCLA LOGIC COLLOQUIUM
                   Friday, November 13, 1992
                           4:00 p.m.
                  Mathematical Sciences 6627
                             UCLA
                                                  
                        LEO HARRINGTON      
                         (UC Berkeley)

  "EXAMPLES OF DEFINABLE CLASSES IN THE LATTICE OF R.E. SETS"

                           Abstract
          
E  is the lattice of recursively enumerable sets under inclusion.  The
techniques for constructing r.e. sets suggest that E  should exhibit
certain saturation-like properties, and these techniques do yield a
methodology for constructing automorphisms of  E, but so far only
Delta^0_3  ones.  Model theory tells us that for countable structures,
automorphisms are directly dual to definable sets (at least in the
infinitary sense of definable).  In several situations over the last
ten years, the failure of the techniques for building automorphisms of
E  has yielded the types of definable sets model theory would predict,
despite the fact that these techniques only involve  Delta^0_3
automorphisms.  Several examples of this nebulous method for producing
a definable set from a failed automorphism construction, will be
presented.