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Unbounded and dominating reals in Hechler extensions

Published online by Cambridge University Press:  12 March 2014

Justin Palumbo
Justin Palumbo*
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90095-1555, USA, E-mail: justinpa@math.ucla.edu
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Abstract

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 Löwe (Conjecture 15 of [4]). We also answer a question due to Laflamme.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 275 - 289
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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