Series: Penn State Logic Seminar Date: Tuesday, April 29, 2003 Time: 2:30 - 3:45 PM Place: 113 McAllister Building Speaker: Christopher Griffin, Penn State, ARL Title: Non-Effective Quantifier Elimination Abstract: We present a short note of the same title from Mihai Prunescu. This note appeared in Math. Log. Quart. 47(4), 2001. Let T be a theory and let E be the property that T admits quantifier elimination, EE be the property that said quantifier elimination is effective and D be the property that the theory is decidable. We will give examples showing that E does not imply EE in the absence of D. In particular, we will use a structure that appears in Math 563 homework to do this. We will also give examples of theories that are undecidable but that have effective quantifier elimination. Background information will be provided if there are a substantial number of audience members unfamiliar with quantifier elimination.