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Two brief formulations of Boolean algebra. (English) Zbl 0060.06303


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[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.
[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. · Zbl 0008.09704
[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. · Zbl 0010.24103
[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. · Zbl 0017.24401
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