Arithmetic with Satisfaction
نویسندگان
چکیده
منابع مشابه
Arithmetic With Satisfaction
A language in which we can express arithmetic and which contains its own satisfaction predicate (in the style of Kripke’s theory of truth) can be formulated using just two nonlogical primitives: ′ (the successor function) and Sat (a satisfaction predicate). Let L be a language with vocabulary: , ( ) ∃ ¬ ∨ = ′ Sat plus the variables x0, x1, x2, . . .. A term is a variable followed by zero or mor...
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We explore the expressivity of constraint satisfaction problems (CSPs) in the arithmetic circuit model. While CSPs are known to yield VNP-complete polynomials in the general case, we show that for different restrictions of the structure of the CSPs we get characterizations of different arithmetic circuit classes. In particular we give the first natural non-circuit characterization of VP, the cl...
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A satisfaction class is a set of nonstandard sentences respecting Tarski’s truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively saturated. A proof of this fact is presente...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1995
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1040248460