Two brief formulations of Boolean algebra
Author:
Lee Byrne
Journal:
Bull. Amer. Math. Soc. 52 (1946), 269272
MathSciNet review:
0016091
Fulltext PDF
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, http://dx.doi.org/10.1090/S00029947191315009601
 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. 783787. 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, http://dx.doi.org/10.1090/S00029947193415017730
 4.
E. V. Huntington, New sets of postulates for the algebra of logic, Trans. Amer. Math. Soc. vol. 35 (1933) pp. 274304, 557558, 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. 588592. Has only one transformation postulate, but this is metamathematical in character, and equivalent to an infinite bundle of "objectlanguage" axioms of the kind considered in this paper.
 1.
 H. M. Sheffer, A set of five independent postulates for Boolean algebras, Trans. Amer. Math. Soc. vol. 14 (1913) pp. 481488. 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. 783787. 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. 876884. 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. 274304, 557558, 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. 588592. Has only one transformation postulate, but this is metamathematical in character, and equivalent to an infinite bundle of "objectlanguage" axioms of the kind considered in this paper.
Additional Information
DOI:
http://dx.doi.org/10.1090/S000299041946085560
PII:
S 00029904(1946)085560
