Description:
Definitions for forms involving conditional choice and variations of Rado's lemma.
Content:
Below are some definitions for forms involving conditional choice and variations of Rado's lemma.
- \(M\) is a binary mess on a set \(S\) if \(M\) is a set offunctions from finite subsets of \(S\) to \(\{0,1\}\) such that for all finite \(P\subseteq S\), there is a \(t\in M\) with domain \(P\) and for all \(t\in M\), and for all finite \(P\subseteq S\), \(t|P\in M\).
- If \(M\) is a binary mess on \(S\), a function \(f: S\to \{0,1\}\) is consistent with \(M\) if \(f|P\in M\) for all finite \(P\subseteq S\).
- If \(f\) is a function and \(R\) a symmetric binary relation, \(f\) is \(R\)-consistent if for all \(x\) and \(y\) in the domain of \(f\),\(f(x)\mathrel R f(y)\).
Howard-Rubin number:
109
Type:
Definitions
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