Geodesic
Todorcevic orderings as examples of ccc forcings without adding random reals
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 125-132.

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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.
DOI : 10.14712/1213-7243.015.111
Classification : 03E17, 03E35
Keywords: Todorcevic orderings; random reals 
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Yorioka, Teruyuki. Todorcevic orderings as examples of ccc forcings without adding random reals. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 125-132. doi : 10.14712/1213-7243.015.111. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.015.111/

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