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Branch of combinatorics with the philosophy that 'total disorder is impossible'. For example, Ramsey's theorem asserts that for each $n$, every sufficiently large graph either contains a clique of size $n$ or a stable set of size $n$.

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 …
Archimondain's user avatar
2 votes
1 answer
117 views

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 …
Archimondain's user avatar