Copies of Monomorphic Structures

Miloš S. Kurilić

Published 2023-12-31Version 1

The poset of copies of relational structure ${\mathbb X}$ is the partial order $\langle {\mathbb P} ({\mathbb X}) ,\subset \rangle$, where ${\mathbb P} ({\mathbb X}):=\{ f[X]: f\in \mathop{\rm Emb}\nolimits ({\mathbb X})\}$. We consider the classifications of structures related to the similarities of their posets of copies, in particular, related to isomorphism of their Boolean completions. The aim of the paper is to extend the known results concerning linear orders to a much larger class of monomorphic structures.