A First-Order Isomorphism Theorem

Authors:
Eric Allender;José Balcázar;Neil Immerman
Affiliations:
-;-;-
Venue:
SIAM Journal on Computing
Year:
1997

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Cited 7

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Abstract

We show that for most complexity classes of interest, all sets complete under first-order projections (fops) are isomorphic under first-order isomorphisms. That is, a very restricted version of the Berman--Hartmanis conjecture holds. Since "natural" complete problems seem to stay complete via fops, this indicates that up to first-order isomorphism there is only one "natural" complete problem for each "nice" complexity class.