Degrees of Models of True Arithmetic

Publisher Summary This chapter discusses the degrees of models of true arithmetic. The chapter presents the proof of a particular theorem that describes a three-worker construction that produces a complete, consistent, Henkinized theory. The chapter introduces a countable model of Peano Arithmetic with binary functions. It discusses Knight's conjecture, analogue of the Jockusch–Soare theorem by using ideas from Harrington's [H] construction of a nonstandard formula. It is assumed via the recursion theorem that each worker knows the others' strategies—that is, a recursive function is actually described.