Linearly ordered sets with only one operator have the amalgamation property

Lipparini, Paolo

doi:10.1016/j.apal.2021.103015

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One Relation With Operators1

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2024

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Cited by 2 publications

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“…Immediate from Proposition 2.1. Item (2) can be easily proved directly (e. g., [L,Corollary 2.4]); anyway, it follows from Remark 2.2 and Proposition 2.1 again.…”

Section: One Relation With Operatorsmentioning

confidence: 95%

Comparable binary relations and the amalgamation property

Lipparini¹

2023

Preprint

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The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity, reflexivity, symmetry, antireflexivity and antisymmetry. The amalgamation property is maintained when we add families of unary operations preserving all the relations. As a consequence, we get the existence of Fraïssé limits for classes of finite structures.The results fail, for general comparability conditions, when three or more binary relations are taken into account, or when we add an operation preserving just one relation.

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“…Immediate from Proposition 2.1. Item (2) can be easily proved directly (e. g., [L,Corollary 2.4]); anyway, it follows from Remark 2.2 and Proposition 2.1 again.…”

Section: One Relation With Operatorsmentioning

confidence: 95%

Comparable binary relations and the amalgamation property

Lipparini¹

2023

Preprint

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The Amalgamation Property for automorphisms of ordered abelian groups

Dobrowolski,

Mennuni

2024

Trans. Amer. Math. Soc.

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We prove that the category of ordered abelian groups equipped with an automorphism has the Amalgamation Property, deduce that their inductive theory is N I P \mathsf {NIP} in the sense of positive logic, and initiate a development of the latter framework. As byproducts of the proof, we obtain a generalised version of the Hahn Embedding Theorem which allows to lift each automorphism of an ordered abelian group to one of an ordered real vector space, and we show that, on existentially closed structures, linear combinations of iterates of the automorphism have the Intermediate Value Property.

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Linearly ordered sets with only one operator have the amalgamation property

Cited by 2 publications

References 14 publications

Comparable binary relations and the amalgamation property

Comparable binary relations and the amalgamation property

The Amalgamation Property for automorphisms of ordered abelian groups

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