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Summary: A First-Order Isomorphism Theorem
Eric Allendery
Department of Computer Science, Rutgers University
New Brunswick, NJ, USA 08903
allender@cs.rutgers.edu
Jos
e Balc
azarz
U. Polit ecnica de Catalunya, Departamento L.S.I.
Pau Gargallo 5, E-08071 Barcelona, Spain
balqui@lsi.upc.es
Neil Immermanx
Computer Science Department, University of Massachusetts
Amherst, MA, USA 01003
immerman@cs.umass.edu
Abstract
We show that for most complexity classes of interest, all sets complete under rst-
order projections fops are isomorphic under rst-order isomorphisms. That is, a very
restricted version of the Berman-Hartmanis Conjecture holds. Since natural" com-
plete problems seem to stay complete via fops, this indicates that up to rst-order
isomorphism there is only one natural" complete problem for each nice" complexity
class.
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