Two brief formulations of Boolean algebra

Author:
Lee Byrne

Journal:
Bull. Amer. Math. Soc. **52** (1946), 269-272

DOI:
https://doi.org/10.1090/S0002-9904-1946-08556-0

MathSciNet review:
0016091

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**1.**H. M. Sheffer,*A set of five independent postulates for Boolean algebras*, Trans. Amer. Math. Soc. vol. 14 (1913) pp. 481-488. This was the first version in which the transformation postulates numbered only three, then a very radical reduction (the other two were "formation" postulates on number of elements and closure). It also showed for the first time that the number of undefined concepts (operations) other than the class of elements could be reduced to one. MR**1500960****2.**B. A. Bernstein,*Simplification of the set of four postulates for Boolean algebras in terms of rejection*, Bull. Amer. Math. Soc. vol. 39 (1933) pp. 783-787. In effect this reduces Sheffer's three transformation postulates to two, employing the same operation.**3.**B. A. Bernstein,*A set of four postulates for Boolean algebras in terms of the "implicative" operation*, Trans. Amer. Math. Soc. vol. 36 (1934) pp. 876-884. Another version in two transformation postulates. MR**1501773****4.**E. V. Huntington,*New sets of postulates for the algebra of logic*, Trans. Amer. Math. Soc. vol. 35 (1933) pp. 274-304, 557-558, 971. The fourth and fifth sets are limited to three transformation postulates.**5.**S. Hoberman and J. C. C. McKinsey,*A set of postulates for Boolean algebra*, Bull. Amer. Math. Soc. vol. 43 (1937) pp. 588-592. Has only*one*transformation postulate, but this is metamathematical in character, and equivalent to an infinite bundle of "object-language" axioms of the kind considered in this paper.

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DOI:
https://doi.org/10.1090/S0002-9904-1946-08556-0