Mac Lane Saunders. Symbolic logic. The American mathematical monthly, vol. 46 (1939), pp. 289–296.

uniquely represented as a finite sum of distinct basis elements. A Boolean ring R is atomic if every element ^0 of R majorizes an atom of R, i.e., an element ?*0 which majorizes only 0; R is hereditarily atomic if every Boolean ring homomorphic to R is atomic. It is shown that the four conditions: (i) R is hereditarily atomic, (ii) every ring homomorphic to R contains an atom, (iii) every subring of R is atomic, (iv) every subring of R contains an atom, are equivalent. If R has an ordered basis then the following equivalences hold: (i) R is hereditarily atomic, (ii) R has a scattered (zerstreut) basis, (iii) every ordered basis of R is scattered. one; the weakening even of the underlying logic, of contra diction. a a series of logical concepts, for These logical formulations for the most part too vague for appraisal; occasional confusions are unmistakable, level account of number of in the foundations of comparing formalism, intuitionism. In several espe the proof of Godel's theorem, the extreme brevity This is a short introduction, for the lay reader, to mathematical logic and its appli cability to the problems of the sciences. After graphically contrasting the non-numerical with the numerical branches of mathematics, Quine compares some of the more important concepts of the logic of propositions and of relations with corresponding notions in numeri cal algebra. The paper concludes with a brief discussion of the applicability of mathe matical logic to problems of technology, and as evidence of its present employment therein he reports on the use of the statement calculus in solving problems in electrical engineering at The Massachusetts Institute of Technology, and in formulating and proving the con sistency of contracts by a large insurance company.