Review of Klein 1931 : On the theory of abstract connectives (1932h)
Solomon Feferman, John W Dawson, Stephen Cole Kleene, Gregory Martin Moore, Robert M Solovay, Jean van HEIJENOORT · 2001
Abstract The author investigates domains of individuals in which two operations, a U b and a n b, are defined and satisfy the axioms of the calculus of classes for union and intersection. The analog of complementation is introduced as a one-to-one symmetric mapping of the domain onto itself, by means of which the two connectives U and n are interchanged. In addition to the calculi of classes and of propositions, the operations max (a, b) and min (a, b), for example, or greatest common divisor and least common multiple, are considered as realizations of the axioms. After derivation of various simple theorems (for example, the uniqueness of the decomposition of elements of the domain into prime elements, if such a decomposition exists at all), what is called a “characteristic” mapping is introduced.