Teruyuki Yorioka
Todorcevic orderings as examples of ccc forcings without adding random reals

Comment.Math.Univ.Carolin. 56,1 (2015) 125-132.

Abstract:In [{\it Two examples of Borel partially ordered sets with the countable chain condition\/}, Proc. Amer. Math. Soc. {\bf 112} (1991), no.~4, 1125--1128], Todorcevic introduced a ccc forcing which is Borel definable in a separable metric space. In [{\it On Todorcevic orderings\/}, Fund. Math., to appear], Balcar, Paz\'ak and Th\"ummel applied it to more general topological spaces and called such forcings {\it Todorcevic orderings\/}. There they analyze Todorcevic orderings quite deeply. A significant remark is that Th\"ummel solved the problem of Horn and Tarski by use of Todorcevic ordering [{\it The problem of Horn and Tarski\/}, Proc. Amer. Math. Soc. {\bf 142} (2014), no.~6, 1997--2000]. This paper supplements the analysis of Todorcevic orderings due to Balcar, Paz\'ak and Th\"ummel in [{\it 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.

Keywords: Todorcevic orderings; random reals

DOI: DOI 10.147.12/1213-7243.015.111
AMS Subject Classification: 03E35 03E17