| Title:
|
Todorcevic orderings as examples of ccc forcings without adding random reals (English) |
| Author:
|
Yorioka, Teruyuki |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
125-132 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In [Two examples of Borel partially ordered sets with the countable chain condition, Proc. Amer. Math. Soc. 112 (1991), no. 4, 1125–1128], Todorcevic introduced a ccc forcing which is Borel definable in a separable metric space. In [On Todorcevic orderings, Fund. Math., to appear], Balcar, Pazák and Thümmel applied it to more general topological spaces and called such forcings Todorcevic orderings. There they analyze Todorcevic orderings quite deeply. A significant remark is that Thümmel solved the problem of Horn and Tarski by use of Todorcevic ordering [The problem of Horn and Tarski, Proc. Amer. Math. Soc. 142 (2014), no. 6, 1997–2000]. This paper supplements the analysis of Todorcevic orderings due to Balcar, Pazák and Thümmel in [On Todorcevic orderings, Fund. Math., to appear]. More precisely, it is proved that Todorcevic orderings add no random reals whenever they have the countable chain condition. (English) |
| Keyword:
|
Todorcevic orderings |
| Keyword:
|
random reals |
| MSC:
|
03E17 |
| MSC:
|
03E35 |
| idZBL:
|
Zbl 06433811 |
| idMR:
|
MR3311583 |
| DOI:
|
10.14712/1213-7243.015.111 |
| . |
| Date available:
|
2015-03-10T17:42:55Z |
| Last updated:
|
2017-04-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144194 |
| . |
| Reference:
|
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