The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory (1940)
Kurt Gudel, Solomon Feferman, John W Dawson, Stephen Cole Kleene, Gregory Martin Moore, Robert M Solovay, Jean van HEIJENOORT · 2001
Abstract In order to define Δ and to prove the above properties of it from the axioms of Σ, it is necessary first to develop abstract set theory to a certain extent from the axioms of Σ-This is done in Chapters II-IV. Although the definitions and theorems are mostly stated in logistic symbols, the theory developed is not to be considered as a formal system but as an axiomatic theory in which the meaning and the properties of the logical symbols are presupposed to be known. However, to everyone familiar with mathematical logic it will be clear that the proofs could be formalized, using only the rules of Hilbert’s “engerer Funktionenkalkul”.