On the Automorphism Group of the Universal Homogeneous Meet-Tree

Kaplan, Itay; Rzepecki, Tomasz; Siniora, Daoud

doi:10.1017/jsl.2021.9

Cited by 2 publications

(2 citation statements)

References 13 publications

(40 reference statements)

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“…They appear in the classification of countable 2‐homogeneous trees from [5], and have since been important in the theory of permutation groups; cf., e.g., [1, 3, 4]. More recently, they were shown to be dp‐minimal in [17], and the automorphism group of the unique countable one was studied in [10], while the interest in similar structures goes back at the very least to [14, 20], where they were used as a base to produce examples in the context of Ehrenfeucht theories. Here we study

\mathsf {DMT}

, and some of the expansions defined in [7], from the viewpoint of domination, in the sense of [13].…”

mentioning

confidence: 99%

Weakly binary expansions of dense meet‐trees

Mennuni

2021

Mathematical Logic Qtrly

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We compute the domination monoid in the theory DMT$\mathsf {DMT}$ of dense meet‐trees. In order to show that this monoid is well‐defined, we prove weak binarity of DMT$\mathsf {DMT}$ and, more generally, of certain expansions of it by binary relations on sets of open cones, a special case being the theory DTR$\mathsf {DTR}$ from [7]. We then describe the domination monoids of such expansions in terms of those of the expanding relations.

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\mathsf {DMT}

, and some of the expansions defined in [7], from the viewpoint of domination, in the sense of [13].…”

mentioning

confidence: 99%

Weakly binary expansions of dense meet‐trees

Mennuni

2021

Mathematical Logic Qtrly

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show abstract

“…They appear in the classification of countable 2-homogeneous trees from [Dro85], and have since been important in the theory of permutation groups, see for instance [Cam87,DHM89,AN98]. More recently, they were shown to be dp-minimal in [Sim11], and the automorphism group of the unique countable one was studied in [KRS19], while the interest in similar structures goes back at the very least to [Per73,Woo78], where they were used as a base to produce examples in the context of Ehrenfeucht theories. Here we study DMT, and some of the expansions defined in [EK19], from the viewpoint of domination, in the sense of [Men20b].…”

mentioning

confidence: 99%