Good books on non-standard logics/set theories.

Question

So, I am looking for good books on intuicionistic logic & set theory theory and on constructive set theories. Does anyone has suggestions?

Background notes: I am familiar with work within ZFC, like proofs connected to L/diamond principles/trees; basic concepts of forcing and related to it consistency proofs; Godel's incompleteness theorems and very basics of model theory.

Answer 1

You can see :

• Anne Troelstra & Dirk van Dalen, Constructivism in mathematics : An Introduction (1988)

and :

• Set Theory : Constructive and Intuitionistic $\mathsf {ZF}$ with many references to other SEP's entries and bibliography.

Also : John Bell, Intuitionistic Set Theory (2014).