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March 2003 Strong extension axioms and Shelah’s zero-one law for choiceless polynomial time
Andreas Blass, Yuri Gurevich
J. Symbolic Logic 68(1): 65-131 (March 2003). DOI: 10.2178/jsl/1045861507

Abstract

This paper developed from Shelah’s proof of a zero-one law for the complexity class “choiceless polynomial time,” defined by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The extension axioms, which form the basis for earlier zero-one laws (for first-order logic, fixed-point logic, and finite-variable infinitary logic) are inadequate in the case of choiceless polynomial time; they must be replaced by what we call the strong extension axioms. We present an extensive discussion of these axioms and their role both in the zero-one law and in general.

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Andreas Blass. Yuri Gurevich. "Strong extension axioms and Shelah’s zero-one law for choiceless polynomial time." J. Symbolic Logic 68 (1) 65 - 131, March 2003. https://doi.org/10.2178/jsl/1045861507

Information

Published: March 2003
First available in Project Euclid: 21 February 2003

zbMATH: 1045.03039
MathSciNet: MR1959313
Digital Object Identifier: 10.2178/jsl/1045861507

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 1 • March 2003
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