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10 votes
1 answer
354 views

Elementary equivalence between $n\mapsto n+1$ and its inverse on the Stone-Čech remainder?

Consider structures $(A,f)$ encoding a Boolean algebra $A$ endowed with an automorphism $f$. There is an obvious notion of isomorphism between such structures. Consider the endomorphism $\hat{\Phi}$ ...
6 votes
1 answer
337 views

Boolean valued models in a general setting

It is well known that Boolean valued models play significant roles for set-theoretic purposes. But how well-studied are Boolean valued models in a more general setting, as models for random first-...
8 votes
1 answer
480 views

Intuition behind Boolean-valued models of set theory

$\DeclareMathOperator\Card{Card}$The book Forcing Eine Einführung in die Mathematik der Unabhängigkeitsbeweise by Hoffmann provides an intuition behind boolean valued models of set theory which I will ...
4 votes
2 answers
625 views

The category of Boolean-valued models associated to a model of ZFC

This is related to my previous question here, and indirectly motivated by Andreas Blass intriguing answer therein: start from a ZF transitive model $M$, and consider the category $CBA(M)$ of ...