Brendle, Jörg Strolling through paradise. (English) Zbl 0835.03010 Fundam. Math. 148, No. 1, 1-25 (1995). Summary: With each of the classical tree-like forcings adjoining a new real, one can associate a \(\sigma\)-ideal on the reals in a natural way. For example, the ideal \(s^0\) of Marczewski null sets corresponds to Sacks forcing \(\mathbb{S}\), while the ideal \(r^0\) of nowhere Ramsey sets corresponds to Mathias forcing \(\mathbb{R}\). We show (in ZFC) that none of these ideals is included in any of the others. We also discuss Mycielski’s ideal \({\mathfrak P}_2\), and start an investigation of the covering numbers of these ideals. Cited in 3 ReviewsCited in 16 Documents MSC: 03E05 Other combinatorial set theory 03E35 Consistency and independence results 03E40 Other aspects of forcing and Boolean-valued models Keywords:\(\sigma\)-ideal; Marczewski ideal; Mycielski ideal; Miller forcing; Laver forcing; Matet forcing; Silver forcing; tree-like forcings adjoining a new real; Sacks forcing; nowhere Ramsey sets; Mathias forcing; covering numbers PDFBibTeX XMLCite \textit{J. Brendle}, Fundam. Math. 148, No. 1, 1--25 (1995; Zbl 0835.03010) Full Text: DOI arXiv EuDML