1
vote
1answer
29 views

If $G$ is a generic ultrafilter, why $(\exists a\in A)(a\in G)\leftrightarrow \Sigma A\in G$?

Let $B$ be a complete Boolean Algebra. Let $G$ be a generic ultrafilter of $B$, that is, such that for any dense $D\subset B$ we have $D\cap G\neq \emptyset$. Why for all $A\subseteq B,$ $\Sigma A\in ...
2
votes
1answer
155 views

Infitive distributive law in boolean valued models

I'm posting the problem 2.14 and 2.15 of the book "Set theory" of J.L. Bell. These problem are proposed after the forcing relation chapter and I'm new in this kind of stuff, so I have some little ...
1
vote
0answers
61 views

$\Delta_0$-formulas in the Boolean-valued model $V^B$

I want to show that $\Vert \check x = \check y \Vert = 1$ implies $x = y$, where $\check x$ is the canonical name for $x$ in $V^B$. I'd like try induction over the ranks of $\check x$ and $\check y$ ...