Maximal Tukey types, P-ideals and the weak Rudin-Keisler order

Konstantinos A. Beros; Paul B. Larson

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arXiv · 1902.00968

Maximal Tukey types, P-ideals and the weak Rudin-Keisler order

Konstantinos A. Beros·Paul B. Larson

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Abstract

In this paper, we study some new examples of ideals on $\omega$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order -- known as the "weak Rudin-Keisler order" -- and its structure when restricted to these ideals of maximal Tukey type. Mirroring a result of Fremlin on the Tukey order, we also show that there is an analytic P-ideal above all other analytic P-ideals in the weak Rudin-Keisler. Acknowledgment: this preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in the Archive for Mathematical Logic, and is available online at https://doi.org/10.1007/s00153-023-00897-z.

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BibTeX RIS

Konstantinos A. Beros, Paul B. Larson. 2019-02-03. Maximal Tukey types, P-ideals and the weak Rudin-Keisler order. https://arxiv.org/abs/1902.00968

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