Church's Thesis is Consistent with Epistemic Arithmetic

Publisher Summary This chapter describes Funayama's theorem for recursive realizability for epistemic arithmetic. It is essentially divided into two parts. The main tool is the notion of adjoints for preordered sets. The chapter considers the usage of the version of the Funayama's theorem and ideas to construct a recursive realizability model for epistemic arithmetic. The main objective is to integrate recursive realizability and the classical notion of truth. This is accomplished by adapting the construction used in the proof of Funayama's theorem. Funayama's theorem asserts that any complete Heyting algebra can be embedded in a complete Boolean algebra by a map that preserves finite infimums and arbitrary supremums. The second part describes the recursive realizability interpretation that provides a useful method for obtaining consistency results for intuitionistic systems.