What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to be no survey paper dealing with their history. This is a follow-up question to a previous question: "Boolean-valued models vs. the Infinite-valued Logic of Lukasiewicz and set theory". Given Chang's result regarding the consistency of the Axiom of Comprehension (at least a version of it) in infinite-valued logic, what motivated the community of set theorists to take the Boolean-valued model route vs. the infinite-valued logic route (though Boolean-valued models might be classified as a type of infinite-valued logic, there are differences)?

3

$\begingroup$
$\endgroup$

Set theory. Boolean-valued models and independence proofs, third edition. Oxford Logic Guides, 47. The Clarendon Press, Oxford University Press, Oxford, 2005. MR2257858 (2007d:03087) $\endgroup$ – Andrés E. Caicedo Nov 23 '12 at 7:16inadequateto develop mathematics, namely Hájek proved that it is inconsistent with induction.) Though if you are asking what motivated the set-theoretical community, I’d guess that most of the community never evenheardof Chang’s result. $\endgroup$ – Emil Jeřábek Nov 23 '12 at 12:08