Description: Definitions for forms [1 L], [1 M], [1 N], [10 C] and [132 A]
Content:
Definitions for forms [1 L], [1 M], [1 N], [10 C] and [132 A]
A set mapping \(f\) is a function \(f : X \to \cal P(X)\) such that for all \(x\in X\), \(x \not \in f(x).\) A free subset of \(X\) (relative to \(f\)) is a subset \(H\) of \(X\) such that for all \(x, y\in H\), \(x\not\in f(y)\). A ramification system is a triple \(\langle X,E,S\rangle\) where \(X\) and \(E\) are sets and \(S : X^{\le\theta} \rightarrow \cal P(E)\) (where \(\theta\) is an ordinal and \(X^{\le\theta}\) denotes all functions \(t: \alpha\to X\) where \(\alpha \le\theta\)) satisfies (i) \(S(\emptyset) = E\) (ii) If \(f, g\in\) dom\((S)\) and \(f\subseteq g\), then \(S(g)\subseteq S(f)\) and (iii) If \(f \in\) dom\((S)\) and \(\eta =\) dom\((f)\) is a limit ordinal then \(S(f) = \bigcap_{\alpha< \eta} S(f/\alpha )\).
Howard-Rubin number: 22
Type: Definitions
Back