Todorcevic orderings as examples of ccc forcings without adding random reals
نویسندگان
چکیده
منابع مشابه
Todorcevic Orderings as Examples of Ccc Forcings without Adding Random Reals
In [13], Todorcevic introduced a ccc forcing which is Borel definable in a separable metric space. In [2], Balcar, Pazák and Thümmel applied it to more general topological spaces and called such forcings Todorcevic orderings. In [2], they analyze Todorcevic orderings quite deeply. A significant remark is that Thümmel solved the problem of Horn and Tarski by use of Todorcevic ordering [11]. This...
متن کاملAdding a Lot of Random Reals by Adding a Few
We study pairs (V, V1) of models of ZFC such that adding κ-many random reals over V1 adds λ-many random reals over V , for some λ > κ.
متن کاملCCC Forcing and Splitting Reals
Prikry asked if it is relatively consistent with the usual axioms of ZFC that every nontrivial ccc forcing adds either a Cohen or a random real. Both Cohen and random reals have the property that they neither contain nor are disjoint from an infinite set of integers in the ground model, i.e. they are splitting reals. In this note I show that that it is relatively consistent with ZFC that every ...
متن کاملSmall Forcings and Cohen Reals
We show that all posets of size א1 may have to add a Cohen real and develop some forcing machinery for obtaining this sort of results.
متن کاملChaotic Orderings of the Rationals and Reals
In this note we prove that there is a linear ordering of the set of real numbers for which there is no monotonic 3-term arithmetic progression. This answers the question (asked by Erdős and Graham) of whether or not every linear ordering of the reals must have a monotonic k-term arithmetic progression for every k.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Commentationes Mathematicae Universitatis Carolinae
سال: 2015
ISSN: 0010-2628,1213-7243
DOI: 10.14712/1213-7243.015.111