Lindenbaum algebras and model companions
Model theory for logic.
Model Theory for Lam Logic
Modèles premiers d'une théorie totalement transcendante
Oligomorphic transformation monoids and homomorphism-homogeneous structures
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 -categoricity and the theory of trees
On cardinalities of algebras of formulas for -categorical theories
On countably compact reduced products, III
On d-finite tuples in random variable structures
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
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 elementary cuts in models of arithmetic
On Kalmar's consistency proof and a generalization of the notion of ...-consistency.
On many-sorted ω-categorical theories
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.
On some conjectures connected with complete sentences
On -categorical theories of abelian groups
On -categorical theories of fields
Orbits of denumerable models of complete theories
Positively prime models over a normal basic set.
Remarks on countable models
Singular properties of Morley rank