| Title:
|
On systems of congruences on principal filters of orthomodular implication algebras (English) |
| Author:
|
Halaš, Radomír |
| Author:
|
Plojhar, Luboš |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
423-435 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices. (English) |
| Keyword:
|
orthoimplication algebra |
| Keyword:
|
orthomodular lattice |
| Keyword:
|
$p$-filter |
| MSC:
|
03B60 |
| MSC:
|
03G25 |
| MSC:
|
06B10 |
| MSC:
|
06C15 |
| idZBL:
|
Zbl 1174.03030 |
| idMR:
|
MR2365325 |
| DOI:
|
10.21136/MB.2007.133966 |
| . |
| Date available:
|
2009-09-24T22:33:13Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133966 |
| . |
| Reference:
|
[1] Abbott, J. C.: Semi-boolean algebra.Mat. Vestnik 4 (1967), 177–198. Zbl 0153.02704, MR 0239957 |
| Reference:
|
[2] Abbott, J. C.: Orthoimplication algebras.Stud. Log. 35 (1976), 173–177. Zbl 0331.02036, MR 0441794, 10.1007/BF02120879 |
| Reference:
|
[3] Beran, L.: Orthomodular Lattices—Algebraic Approach.D. Reidel, Dordrecht, 1985. Zbl 0558.06008, MR 0784029 |
| Reference:
|
[4] Burmeister, P., Maczyński, M.: Orthomodular (partial) algebras and their representations.Demonstr. Math. 27 (1994), 701–722. MR 1319415 |
| Reference:
|
[5] Chajda I., Halaš, R., Kühr, J.: Implication in MV-algebras.Algebra Univers. 52 (2004), 377–382. MR 2120523 |
| Reference:
|
[6] Chajda I., Halaš, R., Kühr, J.: Distributive lattices with sectionally antitone involutions.Acta Sci. (Szeged) 71 (2005), 19–33. MR 2160352 |
| Reference:
|
[7] Chajda, I., Halaš, R., Länger, H.: Orthomodular implication algebras.Int. J. Theor. Phys. 40 (2001), 1875–1884. MR 1860644, 10.1023/A:1011933018776 |
| Reference:
|
[8] Chajda, I., Halaš, R., Länger, H.: Simple axioms for orthomodular implication algebras.Int. J. Theor. Phys. 40 (2004), 911–914. MR 2106354, 10.1023/B:IJTP.0000048587.50827.93 |
| Reference:
|
[9] Halaš, R.: Ideals and D-systems in Orthoimplication algebras.J. Mult.-Val. Log. Soft Comput. 11 (2005), 309–316. Zbl 1078.03050, MR 2160472 |
| Reference:
|
[10] Kalmbach, G.: Orhomodular Lattices.Academic Press, London, 1983. MR 0716496 |
| . |
