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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References | Additional Information

**1.**Henry Maurice Sheffer,*A set of five independent postulates for Boolean algebras, with application to logical constants*, Trans. Amer. Math. Soc.**14**(1913), no. 4, 481–488. MR**1500960**, https://doi.org/10.1090/S0002-9947-1913-1500960-1**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 algebra in terms of the “implicative” operation*, Trans. Amer. Math. Soc.**36**(1934), no. 4, 876–884. MR**1501773**, https://doi.org/10.1090/S0002-9947-1934-1501773-0**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.

Additional Information

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