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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
2
votes
1
answer
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Ramsey type properties of $F_\sigma$ ideals
Let $I \subseteq 2^\omega$ be any $F_\sigma$ ideal containing every finite sets :
$\forall X \in I\ \forall Y \subseteq X\ \text{ we have } Y \in I$
$\forall k\ \forall X_1,\dots,X_k \in I\ X_1 \cup …
2
votes
Ramsey type properties of $F_\sigma$ ideals
Well, a positive answer would have been nice, but unfortunately I think there is an easy argument to build a computable instance of $\mathrm{RT^2_{3,2}}$ whose every solution falls in the summable ide …