Two brief formulations of Boolean algebra
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References
- 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, DOI 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.
- 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, DOI 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
- Journal: Bull. Amer. Math. Soc. 52 (1946), 269-272
- DOI: https://doi.org/10.1090/S0002-9904-1946-08556-0
- MathSciNet review: 0016091