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Oligomorphic transformation monoids and homomorphism-homogeneous structures

Dragan Mašulović, Maja Pech (2011)

Fundamenta Mathematicae

A structure is called homomorphism-homogeneous if every homomorphism between finitely generated substructures of the structure extends to an endomorphism of the structure (P. J. Cameron and J. Nešetřil, 2006). In this paper we introduce oligomorphic transformation monoids in full analogy to oligomorphic permutation groups and use this notion to propose a solution to a problem, posed by Cameron and Nešetřil in 2006, to characterize endomorphism monoids of homomorphism-homogeneous relational structures...

On sets with rank one in simple homogeneous structures

Ove Ahlman, Vera Koponen (2015)

Fundamenta Mathematicae

We study definable sets D of SU-rank 1 in ℳ e q , where ℳ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a ’canonically embedded structure’, which inherits all relations on D which are definable in ℳ e q , and has no other definable relations. Our results imply that if no relation symbol of the language of ℳ has arity higher than 2, then there is a close relationship between triviality of dependence and being a reduct of a binary...

On the number of countable models of stable theories

Predrag Tanović (2001)

Fundamenta Mathematicae

We prove: Theorem. If T is a countable, complete, stable, first-order theory having an infinite set of constants with different interpretations, then I(T,ℵ₀) ≥ ℵ₀.

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