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Fraïssé limits for infinite relational languages (2012)
BibTeX
@MISC{Brooke-taylor12fraïssélimits,
author = {Andrew Brooke-taylor and Damiano Testa},
title = {Fraïssé limits for infinite relational languages},
year = {2012}
}
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Abstract
We study Fraïssé limits for certain Fraïssé classes over infinite relational languages that behave similarly to those for finite languages. These include the Fraïssé classes of finite simplicial complexes, finite hypergraphs, and Sperner families on finite sets. With a natural choice of measure we show that almost all countable structures whose finite substructures lie in such a class are isomorphic to the Fraïssé limit, and a corresponding 0-1 law holds for finite models. In particular, we obtain a new 0-1 law for simplicial complexes, different from the previously known one due to Blass and Harary. 1
