Definability in structures of finite valency
نویسندگان
چکیده
منابع مشابه
Arithmetical definability over finite structures
Arithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability over finite structures, motivated by the correspondence between uniform and . We prove finite analogs of three classic results in arithmetical definability, namely that and TIMES can first-order define PLUS, that and DIVIDES can first-order define TIM...
متن کاملInfinitary Logic and Inductive Definability over Finite Structures
The extensions of first-order logic with a least fixed point operators (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [AV91b] investigated the relation of these two logics in the absence of an ordering, using a mchine ...
متن کاملNatural Definability in Degree Structures
A major focus of research in computability theory in recent years has involved definability issues in degree structures. There has been much success in getting general results by coding methods that translate first or second order arithmetic into the structures. In this paper we concentrate on the issues of getting definitions of interesting, apparently external, relations on degrees that are o...
متن کاملDefinability within structures related to
Let Sq denote the set of squares, and let SQn be the squaring function restricted to powers of n; let ⊥ denote the coprimeness relation. Let Bn(x, y) = (x+y x ) MOD n. For every integer n ≥ 2 addition and multiplication are definable in the structures 〈N;Bn,⊥〉 and 〈N;Bn,Sq〉; thus their elementary theories are undecidable. On the other hand, for every prime p the elementary theory of 〈N;Bp,SQp〉 ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1974
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-81-2-173-181