Games with finitely generated structures

Abstract

We study the abstract Banach-Mazur game played with finitely generated structures instead of open sets. We characterize the existence of winning strategies aiming at a single countably generated structure. We also introduce the concept of weak Fraisse classes, extending the classical Fraisse theory and revealing its relations to our Banach-Mazur game.

arXiv commentLast section extended (16 pages)

Cited by in corpus (7)

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• Weak Fraisse categories
• Hereditarily indecomposable continua as generic mathematical structures
• Universal-homogeneous structures are generic
• Homogeneous isosceles-free spaces
• Generic countably infinite groups
• The Banach--Mazur game and the strong Choquet game in domain theory