A generalization of the incompleteness theorem

Abstract

Publisher Summary This chapter illustrates Godel incompleteness theorem and proves the existence of free formulas not only for systems based on the usual rules of proof but also for systems based on the rule ω. The chapter discusses the systems based on the rule ω rests on the basis of the remark of J. R. Shoenfield that the decomposition of the ∏11 sets into constituents can on several occasions be exploited in the same way as the recursive enumerability of the Σ01sets.