Unbounded and dominating reals in Hechler extensions

Details Unbounded and dominating reals in Hechler extensions Unbounded and dominating reals in Hechler extensions

2012-01-13

arxiv.org/abs/1201.2932v1

Mathematics

Logic

17 pages

Scientific paper

We give results exploring the relationship between dominating and unbounded reals in Hechler extensions, as well as the relationships among the extensions themselves. We show that in the standard Hechler extension there is an unbounded real which is dominated by every dominating real, but that this fails to hold in the tree Hechler extension. We prove a representation theorem for dominating reals in the standard Hechler extension: every dominating real eventually dominates a sandwich composition of the Hechler real with two ground model reals that monotonically converge to infinity. We apply our results to negatively settle a conjecture of Brendle and L\"owe. We also answer a question due to Laflamme.

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