| Title:
|
Weak homogeneity and Pierce’s theorem for $MV$-algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1215-1227 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove a theorem on weak homogeneity of $MV$-algebras which generalizes a known result on weak homogeneity of Boolean algebras. Further, we consider a homogeneity condition for $MV$-algebras which is defined by means of an increasing cardinal property. (English) |
| Keyword:
|
$MV$-algebra |
| Keyword:
|
weak homogeneity |
| Keyword:
|
internal direct product decomposition |
| MSC:
|
06D35 |
| idZBL:
|
Zbl 1164.06315 |
| idMR:
|
MR2280805 |
| . |
| Date available:
|
2009-09-24T11:42:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128141 |
| . |
| Reference:
|
[1] R. Cignoli, I. M. I. D’Ottaviano and D. Mundici: Algebraic Foundations of Many-Valued Reasoning.Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097 |
| Reference:
|
[2] J. Jakubík: Konvexe Ketten in $\ell $-Gruppen.Časopis pěst. mat. 84 (1959), 53–63. MR 0104740 |
| Reference:
|
[3] J. Jakubík: Cardinal properties of lattice ordered groups.Fundamenta Math. 74 (1972), 85–98. MR 0302528, 10.4064/fm-74-2-85-98 |
| Reference:
|
[4] J. Jakubík: Direct product decomposition of MV-algebras.Czechoslovak Math. J. 44 (1994), 725–739. MR 1295146 |
| Reference:
|
[5] J. Jakubík: Generalized cardinal properties of lattices and lattice ordered groups.Czechoslovak Math. J 54 (2004), 1035–1053. MR 2100012, 10.1007/s10587-004-6449-x |
| Reference:
|
[6] J. Jakubík: On a homogeneity condition for $MV$-algebras.Czechoslovak Math. J 56 (2006), 79–97. MR 2206288, 10.1007/s10587-006-0007-7 |
| Reference:
|
[7] R. S. Pierce: A note on complete Boolean algebras.Proc. Amer. Math. Soc. 9 (1958), 892–896. MR 0102487, 10.1090/S0002-9939-1958-0102487-6 |
| Reference:
|
[8] R. S. Pierce: Some questions about complete Boolean algebras.Proc. Sympos. Pure Math. 2 (1961), 129–140. Zbl 0101.27104, MR 0138570 |
| Reference:
|
[9] R. Sikorski: Boolean Algebras.Second Edition, Springer Verlag, Berlin, 1964. Zbl 0123.01303, MR 0126393 |
| . |
