| Title:
|
Some cardinal characteristics of ordered sets (English) |
| Author:
|
Novák, Vítězslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
135-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide. (English) |
| MSC:
|
03E10 |
| MSC:
|
06A06 |
| MSC:
|
06A07 |
| idZBL:
|
Zbl 0927.06001 |
| idMR:
|
MR1614021 |
| . |
| Date available:
|
2009-09-24T10:11:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127405 |
| . |
| Reference:
|
[1] G. Birkhoff: Generalized Arithmetic.Duke Math. Journ. 9 (1942), 283–302. Zbl 0060.12609, MR 0007031, 10.1215/S0012-7094-42-00921-9 |
| Reference:
|
[2] G. Birkhoff: Lattice Theory.3$^{\text{rd}}$ edition. Providence, Rhode Island, 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[3] B. Dushnik, E. W. Miller: Partially Ordered Sets.Am. Journ. Math. 63 (1941), 600–610. MR 0004862, 10.2307/2371374 |
| Reference:
|
[4] F. Hausdorff: Grundzüge der Mengenlehre.Leipzig, 1914. |
| Reference:
|
[5] H. Komm: On the Dimension of Partially Ordered Sets.Am. Journ. Math. 70 (1948), 507–520. Zbl 0037.31903, MR 0025541, 10.2307/2372194 |
| Reference:
|
[6] V. M. Micheev: On sets containing the greatest number of pairwise incomparable Boole vectors.Probl. Kib. 2 (1959), 69–71. (Russian) MR 0123498 |
| Reference:
|
[7] V. Novák: On the Pseudodimension of Ordered Sets.Czechoslovak Math. Journ. 13 (88) (1963), 587–598. MR 0180507 |
| Reference:
|
[8] V. Novák: On the $\omega _{\nu }$-dimension and $\omega _{\nu }$-pseudodimension of Ordered Sets.Ztschr. math. Logik u. Grund. d. Math. 10 (1964), 43–48. MR 0180508, 10.1002/malq.19640100204 |
| Reference:
|
[9] M. Novotný: On Representation of Partially Ordered Sets by means of Sequences of 0’s and 1’s.Čas. pěst. mat. 78 (1953), 61–64. (Czech) MR 0079066 |
| Reference:
|
[10] M. Novotný: Bemerkung über die Darstellung teilweise geordneter Mengen.Spisy přír. fak. Mas. Univ. Brno 369 (1955), 1–8. MR 0082958 |
| Reference:
|
[11] M. Novotný, L. Skula: Über gewisse Topologien auf geordneten Mengen.Fund. Math. 56 (1965), 313–324. MR 0175079, 10.4064/fm-56-3-313-324 |
| Reference:
|
[12] W. Sierpinski: Cardinal and Ordinal Numbers.Warszawa, 1958. Zbl 0083.26803, MR 0095787 |
| Reference:
|
[13] E. Sperner: Ein Satz über Untermengen einer endlichen Menge.Math. Ztschr. 27 (1928), 554–558. 10.1007/BF01171114 |
| . |
