The space of infinite partitions of n as a topological Ramsey space

Julian C. Cano ^[1] ; Carlos A. di Prisco ^[2]
1. [1] Universidad Nacional de Colombia
  
  Universidad Nacional de Colombia
  
  Colombia
2. [2] Universidad de Los Andes
  
  Universidad de Los Andes
  
  Colombia
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 64, Nº. Extra 1, 2022, págs. 23-48
Idioma: inglés
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Resumen
- The Ramsey theory of the space of equivalence relations with infinite quotients defined on the set N of natural numbers is an interesting field of research. We view this space as a topological Ramsey space (E∞, ≤, r) and present a game theoretic characterization of the Ramsey property of subsets of E∞. We define a notion of coideal and consider the Ramsey property of subsets of E∞ localized on a coideal H ⊆ E∞. Conditions a coideal H should satisfy to make the structure (E∞, H, ≤, r) a Ramsey space are presented.
  
  Forcing notions related to a coideal H and their main properties are analyzed.