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.<\/p>\n
[Choiceless Polynomial Time Computation and the Zero-One Law<\/a>] is an abridged version of this paper, and [A New Zero-One Law and Strong Extension Axioms<\/a>] is a popular version of this paper.<\/p>\n","protected":false},"excerpt":{"rendered":" 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 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Microsoft Research","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Journal of Symbolic Logic","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Journal of Symbolic 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