202411142311

Tags : Set Theory

Valuation of a $\mathbb{P}$-name

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Valuation of a $\mathbb{P}-$name associates a set with it. This set is generally not in the model itself, but this association lets us talk about the set using its name. That is, it lets us talk about sets outside the model.

Definition

$\text{val}(\tau ,G)\{\text{val}(\sigma ,G):\exists p\in G(⟨\sigma ,p⟩\in \tau )\}$, we also write ${\tau }_G$ for $\text{val}(\tau ,G)$.

We also must define $\text{val}$ by transfinite recursion on $\tau$.

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References