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Combinatorial consequences of adding Cohen reals. (English) Zbl 0839.03037

Judah, Haim (ed.), Set theory of the reals. Proceedings of a winter institute on set theory of the reals held at Bar-Ilan University, Ramat-Gan (Israel), January 1991. Providence, RI: American Mathematical Society (Distrib.), Isr. Math. Conf. Proc. 6, 583-617 (1993).
This is a useful survey of combinatorial consequences of adding, one, \(\omega_1\) or more Cohen reals to a model of ZFC. A real \(r\) is Cohen over a model \(V\) if it does not belong to any meager Borel subset of \(\mathbb{R}\) that is coded in \(V\). Given a few facts about forcing most of the consequences of adding Cohen reals can be derived using the above definition, and this is the approach that the author takes. Besides the more standard results we find a construction of a Suslin tree from a Cohen real, a nowhere trivial autohomeomorphism of \(\omega^*\) and endowments of the Cohen poset.
A similar survey on the more elusive random reals would also be welcome.
For the entire collection see [Zbl 0821.00016].
Reviewer: K.P.Hart (Delft)

MSC:

03E35 Consistency and independence results
03E05 Other combinatorial set theory
03E15 Descriptive set theory
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