Related papers: Cores over Ramsey structures
A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…
We study finitely homogeneous dependent rosy structures, adapting results of Cherlin, Harrington, and Lachlan proved for $\omega$-stable $\omega$-categorical structures. In particular, we prove that such structures have finite {\th}-rank…
We prove that an $\omega$-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to the clone of projections, and that…
We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…
We prove that every many-sorted $\omega$-categorical theory is completely interpretable in a one-sorted $\omega$-categorical theory. As an application, we give a short proof of the existence of non $G$--compact $\omega$-categorical…
A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; the core companion of a theory $T$ is a model-complete core theory $S$ such that every model…
We show that every free amalgamation class of finite structures with relations and (symmetric) partial functions is a Ramsey class when enriched by a free linear ordering of vertices. This is a common strengthening of the…
We prove that certain classes of metrically homogeneous graphs omitting triangles of odd short perimeter as well as triangles of long perimeter have the extension property for partial automorphisms and we describe their Ramsey expansions.
Under no additional assumptions, in this paper we construct a Ramsey expansion for every category of finite objects with finite small Ramsey degrees. Our construction is based on the relationship between small Ramsey degrees, weak…
It has become obvious in the recent development that the structural Ramsey property is a categorical property: it depends not only on the choice of objects, but also on the choice of morphisms involved. In this paper we explicitely put the…
We derive a new sufficient condition for the existence of {\omega}-categorical universal structures in classes of relational structures with constraints, augmenting results by Cherlin, Shelah, Chi, and Hubi\v{c}ka and Ne\v{s}et\v{r}il.…
We give a characterizations of Ramsey ultrafilters on $\mathscr P(\omega)$ in terms of functions $f:\omega^n\to\omega$ and their ultrafilter extensions. To do this, we prove that for any partition $\mathcal P$ of $[\omega]^n$ there is a…
It is known that a countable $\omega$-categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone…
We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous…
In recent years, there has been much progress in the field of structural Ramsey theory, in particular in the study of big Ramsey degrees. In all known examples of infinite structures with finite big Ramsey degrees, there is in fact a single…
In the parlance of relational structures, the Finite Ramsey Theorem states that the class of all finite chains has the Ramsey property. A classical result of J. Ne\v{s}et\v{r}il and V. R\"{o}dl claims that the class of all finite posets…
We introduce the notion of a {\it semi-retraction}. Given two structures $\A$ and $\B$, $\A$ is a semi-retraction of $\B$ if there exist quantifier-free type respecting maps $f: \B \raw \A$ and $g: \A \raw \B$ such that $f \circ g$ is an…
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
We introduce normal cores, as well as the more general action cores, in the context of a semi-abelian category, and further generalise those to split extension cores in the context of a homological category. We prove that, if the category…
We analyse omega-categorical precompact expansions of particular omega-categorical structures from the viewpoint of amenability of their automorphism groups. The main result of the paper corrects and simplifies Section 3.2 of the first…