منابع مشابه
Comparing classes of finite structures
In many branches of mathematics, there is work classifying a collection of objects, up to isomorphism or other important equivalence, in terms of nice invariants. In descriptive set theory, there is a body of work using a notion of “Borel embedding” to compare the classification problems for various classes of structures (fields, graphs, groups, etc.) [7], [3], [11], [12], [13]. In this work, e...
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A collection C of finite L-structures is a 1-dimensional asymptotic class if for every m ∈ N and every formula φ(x, ȳ), where ȳ = (y1, . . . , ym): (i) There is a positive constant C and a finite set E ⊂ R>0 such that for every M ∈ C and ā ∈ Mm, either |φ(M, ā)| ≤ C, or for some μ ∈ E, ∣∣|φ(M, ā)| − μ|M |∣∣ ≤ C|M | 2 . (ii) For every μ ∈ E, there is an L-formula φμ(ȳ), such that φμ(M) is precis...
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Homogenization is a powerful way of taming a class of finite structures with several interesting applications in different areas, from Ramsey theory in combinatorics to constraint satisfaction problems (CSPs) in computer science, through (finite) model theory. A few sufficient conditions for a class of finite structures to allow homogenization are known, and here we provide a necessary conditio...
متن کاملOn Semi/tame Classes of Finite Structures
We modify the definition of robust chains from [25] as an approach to formalizing the Finite Sub-model Property (see [21], for example) from the perspective of a class of finite structures with a generic model (i.e. having the Amalgamation and Joint-embedding properties). We characterize this formulation, which we call super-robustness, modulo a weaker condition (that is closer to the the situa...
متن کاملExtension Preservation Theorems on Classes of Acyclic Finite Structures
A class of structures satisfies the extension preservation theorem if, on this class, every first order sentence is preserved under extension iff it is equivalent to an existential sentence. We consider different acyclicity notions for hypergraphs (γ, β and α-acyclicity and also acyclicity on hypergraph quotients) and estimate their influence on the validity of the extension preservation theore...
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ژورنال
عنوان ژورنال: Algebra and Logic
سال: 2004
ISSN: 0002-5232
DOI: 10.1023/b:allo.0000048827.30718.2c