| Title:
|
OCA and towers in $\Cal P(\Bbb N)/fin$ (English) |
| Author:
|
Farah, Ilijas |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
861-866 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We shall show that Open Coloring Axiom has different influence on the algebra $\Cal P(\Bbb N)/fin$ than on $\Bbb N^\Bbb N/fin$. The tool used to accomplish this is forcing with a Suslin tree. (English) |
| Keyword:
|
Open Coloring Axiom |
| Keyword:
|
dense sets of reals |
| Keyword:
|
towers |
| Keyword:
|
forcing |
| Keyword:
|
Suslin trees |
| MSC:
|
03E05 |
| MSC:
|
03E35 |
| MSC:
|
03E50 |
| MSC:
|
04A20 |
| MSC:
|
06A05 |
| idZBL:
|
Zbl 0887.03037 |
| idMR:
|
MR1440716 |
| . |
| Date available:
|
2009-01-08T18:28:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118893 |
| . |
| Reference:
|
[1] Abraham U., Rubin M., Shelah S.: On the consistency of some partition theorems for continuous colorings, and the structure of $\aleph_1$-dense real order types.Ann. of Pure and Appl. Logic 29 (1985), 123-206. MR 0801036 |
| Reference:
|
[2] Baumgartner J.: All $\aleph_1$-dense sets of reals can be isomorphic.Fundamenta Mathematicae 79 (1973), 100-106. Zbl 0274.02037, MR 0317934 |
| Reference:
|
[3] Devlin K., Johnsbråten H.: The Souslin Problem.Springer Lecture Notes in Mathematics, # 405 (1974). MR 0384542 |
| Reference:
|
[4] Dordal P.L.: Towers in $[ømega]^ømega$ and $^ømegaømega$.Ann. of Pure and Appl. Logic 247-277 (1989), 45.3. MR 1032832 |
| Reference:
|
[5] Fremlin D.: Consequences of Martin's Axiom.Cambridge University Press (1984). Zbl 0551.03033 |
| Reference:
|
[6] Gruenhage G.: Cosmicity of cometrizable spaces.Trans. AMS 313 (1989), 301-315. Zbl 0667.54012, MR 0992600 |
| Reference:
|
[7] Todorčević S.: Partition Problems in Topology.AMS Providence, Rhode Island (1989). MR 0980949 |
| Reference:
|
[8] Todorčević S.: Oscillations of sets of integers.to appear. MR 1601383 |
| Reference:
|
[9] Veličković B.: OCA and automorphisms of $\Cal P(ømega)/fin$.Topology Appl. 49 (1993), 1-13. MR 1202874 |
| Reference:
|
[10] Weese M.: personal communication.. |
| . |
