| Title:
|
On free $MV$-algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
311-317 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we show that free $MV$-algebras can be constructed by applying free abelian lattice ordered groups. (English) |
| Keyword:
|
$MV$-algebra |
| Keyword:
|
abelian lattice ordered group |
| Keyword:
|
free generators |
| MSC:
|
03G20 |
| MSC:
|
06D35 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 1024.06004 |
| idMR:
|
MR1983454 |
| . |
| Date available:
|
2009-09-24T11:01:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127802 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice Theory., Providence, 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[2] R. Cignoli, I M. I. d’Ottaviano and D. Mundici: Algebraic Foundations of Many-Valued Reasoning.Trends in Logic, Studia logica library Vol. 7, Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097 |
| Reference:
|
[3] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[4] D. Gluschankof: Cyclic ordered groups and $MV$-algebras.Czechoslovak Math. J. 43 (1993), 249–263. Zbl 0795.06015, MR 1211747 |
| Reference:
|
[5] J. Jakubík: Direct product decompositions of $MV$-algebras.Czechoslovak Math. J. 44 (1994), 725–739. |
| Reference:
|
[6] R. McNaughton: A theorem about infinite valued sentential logic.J. Symbolic Logic 16 (1951), 1–13. Zbl 0043.00901, MR 0041799, 10.2307/2268660 |
| Reference:
|
[7] D. Mundici: Interpretation of $AFC^*$-algebras in Łukasiewicz sentential calculus.J. Funct. Anal. 65 (1986), 15–63. MR 0819173, 10.1016/0022-1236(86)90015-7 |
| Reference:
|
[8] E. C. Weinberg: Free lattice ordered abelian groups.Math. Ann. 151 (1963), 187–199. Zbl 0114.25801, MR 0153759, 10.1007/BF01398232 |
| Reference:
|
[9] E. C. Weinberg: Free lattice ordered abelian groups, II.Math. Ann. 159 (1965), 217–222. Zbl 0138.26201, MR 0181668, 10.1007/BF01362439 |
| . |
