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Two Fra\"iss\'e-style theorems for homomorphism-homogeneous relational structures

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arxiv 1812.01934 v2 pith:ZAVT3W6D submitted 2018-12-05 math.LO math.CO

Two Fra\"iss\'e-style theorems for homomorphism-homogeneous relational structures

Thomas D. H. Coleman This is my paper
classification math.LO math.CO
keywords homomorphism-homogeneousresultscasecasesclassifiedcompletelycountablecover
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In this paper, we state and prove two Fra\"{i}ss\'{e}-style results that cover existence and uniqueness properties for twelve of the eighteen different notions of homomorphism-homogeneity as introduced by Lockett and Truss, and provide forward directions and implications for the remaining six cases. Following these results, we completely determine the extent to which the countable homogeneous undirected graphs (as classified by Lachlan and Woodrow) are homomorphism-homogeneous; we also provide some insight into the directed graph case.

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