منابع مشابه
A Hanf number for saturation and omission: the superstable case
Suppose t = (T, T1, p) is a triple of two theories in vocabularies τ ⊂ τ1 with cardinality λ and a τ1-type p over the empty set. We show the Hanf number for the property: ‘There is a model M1 of T1 which omits p, but M1 τ is saturated’ is less than i (2(2 λ)+ ) + if T is superstable. We showed in [BS11] that with no stability restriction the Hanf number is essentially equal to the Löwenheim num...
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We study amalgamation properties in a family of abstract elementary classes that we call coloring classes. The family includes the examples previously studied in [3]. We establish that the amalgamation property is equivalent to the disjoint amalgamation property in all coloring classes; find the Hanf number for the amalgamation property for coloring classes; and improve the results of [3] by sh...
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Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...
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Induced saturation number
In this paper, we discuss the induced saturation number. It is a nice generalization of the saturation number that will allow us to consider induced subgraphs. We define the induced saturation number, indsat(n,H), to be the fewest number of gray edges in a trigraph T such that H does not appear in any realization of T , but if a black or white edge of T is flipped to gray then there exists a re...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2011
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm213-3-5