Todorcevic orderings as examples of ccc forcings without adding random reals

Teruyuki Yorioka

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 1, page 125-132
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Yorioka, Teruyuki. "Todorcevic orderings as examples of ccc forcings without adding random reals." Commentationes Mathematicae Universitatis Carolinae 56.1 (2015): 125-132. <http://eudml.org/doc/269869>.

@article{Yorioka2015,
abstract = {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.},
author = {Yorioka, Teruyuki},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Todorcevic orderings; random reals; Todorcevic orderings; random reals},
language = {eng},
number = {1},
pages = {125-132},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Todorcevic orderings as examples of ccc forcings without adding random reals},
url = {http://eudml.org/doc/269869},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Yorioka, Teruyuki
TI - Todorcevic orderings as examples of ccc forcings without adding random reals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 1
SP - 125
EP - 132
AB - 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.
LA - eng
KW - Todorcevic orderings; random reals; Todorcevic orderings; random reals
UR - http://eudml.org/doc/269869
ER -

References

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