Geodesic
Keeping the covering number of the null ideal small
Teruyuki Yorioka1
1 Department of Mathematics Shizuoka University Ohya 836, Shizuoka, 422-8529, Japan
Fundamenta Mathematicae, Tome 231 (2015) no. 2, pp. 139-159.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It is proved that ideal-based forcings with the side condition method of Todorcevic (1984) add no random reals. By applying Judah–Repický's preservation theorem, it is consistent with the covering number of the null ideal being $\aleph _1$ that there are no $S$-spaces, every poset of uniform density $\aleph _1$ adds $\aleph _1$ Cohen reals, there are only five cofinal types of directed posets of size $\aleph _1$, and so on. This extends the previous work of Zapletal (2004).
DOI : 10.4064/fm231-2-3
Keywords: proved ideal based forcings side condition method todorcevic random reals applying judah repick preservation theorem consistent covering number null ideal being aleph there s spaces every poset uniform density aleph adds aleph cohen reals there only five cofinal types directed posets size aleph extends previous work zapletal

Teruyuki Yorioka 1

1 Department of Mathematics Shizuoka University Ohya 836, Shizuoka, 422-8529, Japan 
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Teruyuki Yorioka. Keeping the covering number of the null ideal small. Fundamenta Mathematicae, Tome 231 (2015) no. 2, pp. 139-159. doi : 10.4064/fm231-2-3. http://geodesic.mathdoc.fr/articles/10.4064/fm231-2-3/

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