Higher degrees of distributivity and completeness in Boolean algebras
Authors:
E. C. Smith and Alfred Tarski
Journal:
Trans. Amer. Math. Soc. 84 (1957), 230-257
MSC:
Primary 02.0X
DOI:
https://doi.org/10.1090/S0002-9947-1957-0084466-4
MathSciNet review:
0084466
Full-text PDF Free Access
References | Similar Articles | Additional Information
- [1] Garrett Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, vol. 25, revised edition, American Mathematical Society, New York, N. Y., 1948. MR 0029876
- [2] C. C. Chang, Bull. Amer. Math. Soc. Abstract 61-4-579 (1955).
- [3] Shizu Enomoto, Boolean algebras and fields of sets, Osaka Math. J. 5 (1953), 99–115. MR 56662
- [4] P. Erdös and A. Tarski, On families of mutually exclusive sets, Ann. of Math. (2) 44 (1943), 315–329. MR 8249, https://doi.org/10.2307/1968767
- [5] Alfred Horn and Alfred Tarski, Measures in Boolean algebras, Trans. Amer. Math. Soc. 64 (1948), 467–497. MR 28922, https://doi.org/10.1090/S0002-9947-1948-0028922-8
- [6] R. S. Pierce, Distributivity in Boolean algebras, Pacific J. Math. 7 (1957), 983–992. MR 89180
- [7] Dana Scott, The independence of certain distributive laws in Boolean algebras, Trans. Amer. Math. Soc. 84 (1957), 258–261. MR 86048, https://doi.org/10.1090/S0002-9947-1957-0086048-7
- [8] Roman Sikorski, On the representation of Boolean algebras as fields of sets, Fund. Math. 35 (1948), 247–258. MR 28374, https://doi.org/10.4064/fm-35-1-247-258
- [9] Edgar C. Smith Jr., A distributivity condition for Boolean algebras, Ann. of Math. (2) 64 (1956), 551–561. MR 86047, https://doi.org/10.2307/1969602
- [10] A Tarski, Ideate in vollständigen Mengenkörpern, part I, Fund. Math. vol. 32 (1939) pp. 45-63; part II, Fund. Math. vol. 33 (1945) pp. 51-65.
- [11] -, Über additive und multiplikative Mengenkörpern und Mengenfunktionen, Comptes rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 30 (1937) pp. 151-181.
- [12] -, Sur les classes d'ensembles closes par rapport à certaines opérations élémentaires, Fund. Math. vol. 16 (1930) pp. 181-304.
- [13] Alfred Tarski, Axiomatic and algebraic aspects of two theorems on sums of cardinals, Fund. Math. 35 (1948), 79–104. MR 29955, https://doi.org/10.4064/fm-35-1-79-104
- [14] -, Zur Grundlegung der Boole'schen algebra, Fund. Math. vol. 24 (1935) pp. 177-198.
- [15] -, Cardinal algebras, New York, 1949.
- [16] -, Über unerreichbare Kardinalzahlen, Fund. Math. vol. 30 (1938) pp. 68-89.
- [17] -, Drei Überdeckungssätze der allgemeinen Mengenlehre, Fund. Math. vol. 30 (1938) pp. 132-155.
- [18] S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. vol. 16 (1930) pp. 140-150.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1957-0084466-4
Article copyright:
© Copyright 1957
American Mathematical Society