Authors:John Truss, Edith Vargas-García Pages: 1 - 22 Abstract: We extend results from an earlier paper giving reconstruction results for the endomorphism monoid of the rational numbers under the strict and reflexive relations to the first order reducts of the rationals and the corresponding polymorphism clones. We also give some similar results about the coloured rationals. PubDate: 2021-06-29 Issue No:Vol. 16, No. 2 (2021)
Authors:Martino Lupini Pages: 23 - 35 Abstract: We present a Fraïssé-theoretic perspective on the study of the Poulsen simplex and its properties. PubDate: 2021-06-29 Issue No:Vol. 16, No. 2 (2021)
Authors:Michael Pinsker, Manuel Bodirsky Pages: 36 - 45 Abstract: Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical functions in certain sets using topological dynamics, providing a shorter alternative to the original combinatorial argument. We moreover present equivalent algebraic characterisations of canonicity. PubDate: 2021-06-29 Issue No:Vol. 16, No. 2 (2021)
Authors:Jan Hubička, Matěj Konečný, Jaroslav Nešetřil Pages: 46 - 70 Abstract: We give Ramsey expansions of classes of generalised metric spaces where distances come from a linearly ordered commutative monoid. This complements results of Conant about the extension property for partial automorphisms and extends an earlier result of the first and the last author giving the Ramsey property of convexly ordered $S$-metric spaces. Unlike Conant's approach, our analysis does not require the monoid to be semiarchimedean. PubDate: 2021-06-29 Issue No:Vol. 16, No. 2 (2021)
Authors:Andres Aranda, David Bradley-Williams, Eng Keat Hng, Jan Hubička, Miltiadis Karamanlis, Michael Kompatscher, Matěj Konečný, Micheal Pawliuk Pages: 71 - 89 Abstract: 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. PubDate: 2021-06-29 Issue No:Vol. 16, No. 2 (2021)
Authors:Claude Laflamme, Maurice Pouzet, Norbert Sauer, Robert Woodrow Pages: 90 - 127 Abstract: A sibling of a relational structure $R$ is any structure $S$ which can be embedded into $R$ and, vice versa, such that $R$ can be embedded into $S$. Let $\operatorname{sib}(R)$ be the number of siblings of $R$, these siblings being counted up to isomorphism. Thomassé conjectured that for countable relational structures made of at most countably many relations, $\operatorname{sib}(R)$ is either one, countably infinite, or the size of the continuum; but even showing the special case $\operatorname{sib}(R)1$ is one or infinite is unsettled when $R$ is a countable tree. We prove that if $R$ is countable and $\aleph_{0}$-categorical, then indeed $\operatorname{sib}(R)$ is one or infinite. Furthermore, $\operatorname{sib}(R)$ is one if and only if $R$ is finitely partitionable in the sense of Hodkinson and Macpherson [14]. The key tools in our proof are the notion of monomorphic decomposition of a relational structure introduced in [35] and studied further in [23], [24], and a result of Frasnay [11]. PubDate: 2021-06-29 Issue No:Vol. 16, No. 2 (2021)
Authors:Lionel Nguyen van Thé Pages: 128 - 136 Abstract: The workshop ”Homogeneous Structures, A Workshop in Honour of Norbert Sauer‘s 70th Birthday” took place at the Banff International Research Station from November 8th to November 13th, 2015. The purpose of the following note is to gather the list of open problems that were posed during the problem sessions. Contributions appear in alphabetical order, according to the name of their autho PubDate: 2021-06-29 Issue No:Vol. 16, No. 2 (2021)
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