Decision Problems and Some Solutions

Abstract

Viewed as a collection of sentences, any first-order theory of sets is recursively enumerable: this is an advantage ensuing from the axiomatic method. To restate it, a list of all sentences provable in the theory can be generated through an automatic (infinite) process. Moreover, a reliable certification of theoremhood (that is, a formal derivation from the axioms of the theory) can come along with each sentence in the list.