Every polynomial-time 1-degree collapses if and only if P = PSPACE

Journal of Symbolic Logic 69 (3):713-741 (2004)

Abstract
A set A is m-reducible to B if and only if there is a polynomial-time computable function f such that, for all x, x∈ A if and only if f ∈ B. Two sets are: 1-equivalent if and only if each is m-reducible to the other by one-one reductions; p-invertible equivalent if and only if each is m-reducible to the other by one-one, polynomial-time invertible reductions; and p-isomorphic if and only if there is an m-reduction from one set to the other that is one-one, onto, and polynomial-time invertible. In this paper we show the following characterization. Theorem The following are equivalent: P = PSPACE. Every two 1-equivalent sets are p-isomorphic. Every two p-invertible equivalent sets are p-isomorphic.
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DOI http://projecteuclid.org/euclid.jsl/1096901763
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Creative Sets.John Myhill - 1955 - Mathematical Logic Quarterly 1 (2):97-108.
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