Journal of Symbolic Logic

Strong extension axioms and Shelah’s zero-one law for choiceless polynomial time

Andreas Blass and Yuri Gurevich

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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.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 1 (2003), 65-131.

Dates
First available in Project Euclid: 21 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1045861507

Digital Object Identifier
doi:10.2178/jsl/1045861507

Mathematical Reviews number (MathSciNet)
MR1959313

Zentralblatt MATH identifier
1045.03039

Citation

Blass, Andreas; Gurevich, Yuri. Strong extension axioms and Shelah’s zero-one law for choiceless polynomial time. J. Symbolic Logic 68 (2003), no. 1, 65--131. doi:10.2178/jsl/1045861507. https://projecteuclid.org/euclid.jsl/1045861507


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