| Title:
|
On strong regularity of relations (English) |
| Author:
|
Šlapal, Josef |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
151-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
There exists a natural extension of the notion of preorder from binary relations onto relations whose arities are arbitrary ordinals. In the article we find a condition under which extended preorders coincide with preorders if viewed categorically. (English) |
| Keyword:
|
relations of type $\alpha$ |
| Keyword:
|
reflexivity |
| Keyword:
|
diagonality |
| Keyword:
|
strong regularity |
| Keyword:
|
homomorphism |
| Keyword:
|
extended preorders |
| MSC:
|
03E20 |
| MSC:
|
04A05 |
| MSC:
|
08A02 |
| idZBL:
|
Zbl 0807.04001 |
| idMR:
|
MR1293248 |
| DOI:
|
10.21136/MB.1994.126076 |
| . |
| Date available:
|
2009-09-24T21:04:30Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126076 |
| . |
| Reference:
|
[1] Y. Bar-Hillel A.A. Fraenkel A. Levy: Foundations of Set Theory.North Holland, Amsterdam, 1973. MR 0345816 |
| Reference:
|
[2] E. Čech: Topological papers of Eduard Čech, Ch. 8.Academia, Prague, 1968, pp. 436-472. MR 0248705 |
| Reference:
|
[3] H. Herrlich: Cartesian closed topological categories.Math. Coll. Univ. Cape Town 9 (1974), 1-16. Zbl 0318.18011, MR 0460414 |
| Reference:
|
[4] S. Mac Lane: Categories for the Working Mathematician.Springer-Verlag, Heidelberg-New York, 1971. Zbl 0232.18001, MR 0354798 |
| Reference:
|
[5] V. Novák: On a power of relational structures.Czech. Math. J. 35 (1985), 167-172. MR 0779345 |
| Reference:
|
[6] J. Šlapal: Relations of type $\alpha$.Zeitschr. f. math. Logik und Grundl. d. Math. 34 (1988), 563-573. MR 0973399, 10.1002/malq.19880340608 |
| Reference:
|
[7] J. Šlapal: Cartesian closedness in categories of relational systems.Arch. Math. (Basel) 52 (1989), 603-606. MR 1007636, 10.1007/BF01237574 |
| Reference:
|
[8] J. Šlapal: Relations and topologies.Czech. Math. J. 43 (1993), 141-150. MR 1205237 |
| . |
