Constructive reverse mathematics aims to decompose mathematical theorems into choice principles and logical principles. In this talk, we decompose a version of weak Koenig's lemma with a uniqueness condition called WKL!!.

We discuss classical realizability, a branch of mathematical logic that investigates the computational content of mathematical proofs by establishing a correspondence between proofs and programs. Research in this field has led to the development of highly technical constructions generalizing the method of forcing in set theory. In particular, models of realizability are models of ZF, and forcing models are special cases of realizability models.