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Postulates for Boolean algebra in terms of Ternary rejection
| Content Provider | Semantic Scholar |
|---|---|
| Author | Whiteman, Albert Leon |
| Copyright Year | 1937 |
| Abstract | 1. Introduction. The operation of ternary rejection {in Boolean algebra is the operation () given by (abc) = a'b' + b'c'-\-c'a'. In this paper, I shall present a set of postulates for Boolean algebras in which ternary rejection is taken as the only primitive idea, besides that of class. As a result, all the special Boolean elements are introduced with an elegance not possible in any other set known to the author. Thus, the negative of an element is defined in terms of the primitive ideas, and then any two contradictory elements are chosen to represent the zero element and the universe element of the resulting Boolean algebra. We prove the sufficiency of the new postulates for Boolean algebra by deriving from them the well known Whitehead-Huntington set; § the proof of necessariness consists in the converse derivation. Finally, we establish the consistency and independence of the postulates by furnishing proof-systems of the usual type. |
| Starting Page | 293 |
| Ending Page | 298 |
| Page Count | 6 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9904-1937-06538-4 |
| Alternate Webpage(s) | http://www.ams.org/journals/bull/1937-43-04/S0002-9904-1937-06538-4/S0002-9904-1937-06538-4.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9904-1937-06538-4 |
| Volume Number | 43 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
