In Set Theory p. 209 - Jech (2003), the Jech performs the following construction:
Let $ B \in \mathbf{BoolAlg} $. For $ \alpha \in \mathbf{Ord} $ and $ \lambda \in \mathbf{Lim} $, let
- $ V_0 = \emptyset $,
- $ V_{\alpha^+} = \left\{ x : \operatorname{dom} x \to B \mid \operatorname{dom} x \subseteq V_\alpha \right\} $,
- $ V_\lambda = \bigcup_{\kappa < \lambda} V_\kappa $,
and let $ V = \bigcup_\alpha V_\alpha $.
Is there any name for this $ V $ - perhaps in particular with $ B = 2 $? Any answers appreciated! :)