Maja Pech

Fraïssé Limits in Comma Categories

Fraïssé’s theorem characterizing the existence of universal homogeneous structures is a cornerstone of model theory. A categorical version of these results was developed by Droste and Göbel. Such an abstract version of Fraïssé theory allows to construct unusual objects that are far away from the usual structures. In this paper we are going to derive sufficient conditions for a comma category to contain universal homogeneous objects. Using this criterion, we characterize homogeneous structures that possess universal homogeneous endomorphisms. The existence of such endomorphisms helps to reduce questions about the full endomorphism monoid to the self-embedding monoid of the structure. As another application we characterize the retracts of homogeneous structures that are induced by universal homogeneous retractions. This extends previous results by Bonato, Delić, Mudrinski, Dolinka, and Kubiś.

Reconstructing the Topology of the Elementary Self-embedding Monoids of Countable Saturated Structures

Every transformation monoid comes equipped with a canonical topology, the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This phenomenon is called automatic homeomorphicity. In this paper we show that whenever the automorphism group of a countable saturated structure has automatic homeomorphicity and a trivial center, then the monoid of elementary self-embeddings has automatic homeomorphicity, too. As a second result we strengthen a result by Lascar by showing that whenever

Local Methods for Relational Structures and their Weak Krasner Algebras

{\mathbf {A}}

Endolocality meets homomorphism-homogeneity: a new approach in the study of relational algebras

A is a countable

Universal homogeneous constraint structures and the hom-equivalence classes of weakly oligomorphic structures

\aleph _0

Local methods for Rosenberg relations

ℵ0-categorical G-finite structure whose automorphism group has a trivial center and if