منابع مشابه
Effectively Existentially-Atomic Structures
The notions we study in this paper, those of existentially-atomic structure and effectively existentially-atomic structure, are not really new. The objective of this paper is to single them out, survey their properties from a computability-theoretic viewpoint, and prove a few new results about them. These structures are the simplest ones around, and for that reason alone, it is worth analyzing ...
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The theory of abelian totally ordered groups has a model completion. We show that the theory of abelian lattice-ordered groups has no model companion. Indeed, the Archimedean property can be captured by a first order V3V sentence for existentially complete abelian lattice-ordered groups, and distinguishes between finitely generic abelian lattice-ordered groups and infinitely generic ones. We th...
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A triangle-free graph G is called k-existentially complete if for every induced k-vertex subgraph H of G, every extension of H to a (k+ 1)-vertex triangle-free graph can be realized by adding another vertex of G to H. Cherlin [8, 9] asked whether k-existentially complete triangle-free graphs exist for every k. Here we present known and new constructions of 3existentially complete triangle-free ...
متن کاملWreath Products and Existentially Complete Solvable Groups
It is known that the theory of abelian groups has a model companion but that the theory of groups does not. We show that for any fixed 22 a 2 the theory of groups solvable of length s 22 has no model companion. For the metabelian case (22 = 2) we prove the stronger result that the classes of finitely generic, infinitely generic, and existentially complete metabelian groups are all distinct. We ...
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The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$ does not interpret Robinson's theory $R$. To this end, we borrow tools from model theory---specifically, we investigate model-theoretic properties of the mode...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1974
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-30-1-7-13