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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 d-finite tuples in random variable structures

Shichang Song (2013)

Fundamenta Mathematicae

We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.

On d-finiteness in continuous structures

Itaï Ben Yaacov, Alexander Usvyatsov (2007)

Fundamenta Mathematicae

We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may behave as infinite tuples in classical model theory. The notion of a d-finite tuple attempts to capture some aspects of the classical finite tuple behaviour. We show that many classical results involving finite tuples are valid in continuous logic upon replacing "finite" with "d-finite". Other results,...

On many-sorted ω-categorical theories

Enrique Casanovas, Rodrigo Peláez, Martin Ziegler (2011)

Fundamenta Mathematicae

We prove that every many-sorted ω-categorical theory is completely interpretable in a one-sorted ω-categorical theory. As an application, we give a short proof of the existence of non-G-compact ω-categorical theories.

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