Journal of Symbolic Logic

Unbounded and dominating reals in Hechler extensions

Justin Palumbo

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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.

Article information

Source
J. Symbolic Logic, Volume 78, Issue 1 (2013), 275-289.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1358951114

Digital Object Identifier
doi:10.2178/jsl.7801190

Mathematical Reviews number (MathSciNet)
MR3087076

Zentralblatt MATH identifier
1278.03083

Citation

Palumbo, Justin. Unbounded and dominating reals in Hechler extensions. J. Symbolic Logic 78 (2013), no. 1, 275--289. doi:10.2178/jsl.7801190. https://projecteuclid.org/euclid.jsl/1358951114


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