Banach-Mazur game played in partially ordered sets
Wieslaw Kubi\'s
TL;DR
This paper introduces a variant of the Banach-Mazur game adapted for partially ordered sets, demonstrating its utility in proving universality in Fraisse limits and related structures.
Contribution
It develops a new game-theoretic framework for partially ordered sets and applies it to establish universality results more simply.
Findings
Simplified proofs of universality for Fraisse limits
Extension of Banach-Mazur game to posets
Application to broader classes beyond Fraisse limits
Abstract
We present a version of the Banach-Mazur game, where open sets are replaced by elements of a fixed partially ordered set. We show how to apply it in the theory of Fraisse limits and beyond, obtaining simple proofs of universality of certain objects and classes.
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