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A set of four independent postulates for Boolean algebras
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bernstein, Bruce A. |
| Copyright Year | 1916 |
| Abstract | In these T r a n s a c t i o n s, October, 1913, Sheffert presented the following set of independent postulates for Boole's logic: I. There are at least two distinct K-elements. II. Whenever a and b are K-elements, a I b is a K-element. Definition. a' = a la. III. Whenever a and the indicated combinations of a are K-elements, (a')' = a. IV. Whenever a, b, and the indicated combinations of a and b are Kelements, al(blb') = a'. V. Whenever a, b, c, and the indicated combinations of a, b, and c are K-elements, [ al (blc)]' = (b'la) I (c'la) . This is the most economical set of postulates that has so far been proposed for Boolean algebras. Not only is the number of primitive propositions considerably smaller than that of the smallest sett of previous date-five instead of nine-but also the special elements "zero," the "whole," and the "negative" are all defined and their properties deduced. This economy Dr. Sheffer effected by basing the algebra on the powerful operation of "rejection," .? Choosing the primitive ideas that Dr. Sheffer chose, I give below a set of four independent postulates from which his five Postulates I-V are easily deduced. |
| Starting Page | 50 |
| Ending Page | 52 |
| Page Count | 3 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-1916-1501029-5 |
| Volume Number | 17 |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1916-017-01/S0002-9947-1916-1501029-5/S0002-9947-1916-1501029-5.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9947-1916-1501029-5 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
