Construction of existentially closed Abelian lattice-ordered groups using upper extensions
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DOI: 10.1007/s00012-018-0531-y
Abstract: The upper extension construction of Ball, Conrad, and Darnel is used to produce new examples of non-Archimedean existentially closed Abelian lattice-ordered groups and boundedly existentially closed Abelian lattice-ordered groups. Also given are conditions under which… read more here.
Keywords: existentially closed; lattice ordered; abelian lattice; ordered groups ... See more keywords
On the existence of $$\kappa $$κ-existentially closed groups
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DOI: 10.1007/s00013-018-1213-x
Abstract: We prove that a $$\kappa $$κ-existentially closed group of cardinality $$\lambda $$λ exists whenever $$\kappa \le \lambda $$κ≤λ are uncountable cardinals with $$\lambda ^{ read more here.
Keywords: existentially closed; kappa existentially; group cardinality; closed group ... See more keywords
Further Results on Existentially Closed Graphs Arising from Block Designs
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DOI: 10.1007/s00373-019-02036-z
Abstract: A graph is n-existentially closed (n-e.c.) if for any disjoint subsets A, B of vertices with $$\left| {A \cup B} \right| =n$$A∪B=n, there is a vertex $$z \notin A \cup B$$z∉A∪B adjacent to every vertex… read more here.
Keywords: existentially closed; graphs; block; intersection graphs ... See more keywords
Forcing Formulas in Fraïssé Structures and Classes
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DOI: 10.1007/s10469-018-9509-2
Abstract: We come up with a semantic method of forcing formulas by finite structures in an arbitrary fixed Fraïssé class . Both known and some new necessary and sufficient conditions are derived under which a given… read more here.
Keywords: existentially closed; forcing structure; forcing formulas; structure forcing ... See more keywords
κ-Existentially closed groups ☆
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DOI: 10.1016/j.jalgebra.2017.12.005
Abstract: Abstract Let κ be an infinite cardinal. The class of κ-existentially closed groups is defined and their basic properties are studied. Moreover, for an uncountable cardinal κ, uniqueness of κ-existentially closed groups are shown, provided… read more here.
Keywords: existentially closed; closed groups;