A microscopic approach to Souslin-tree constructions, Part I

Ari Meir Brodsky; Assaf Rinot

doi:10.1016/j.apal.2017.05.003

A microscopic approach to Souslin-tree constructions, Part I

Ari Meir Brodsky, Assaf Rinot

Department of Mathematics

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21 Scopus citations

Abstract

We propose a parameterized proxy principle from which κ-Souslin trees with various additional features can be constructed, regardless of the identity of κ. We then introduce the microscopic approach, which is a simple method for deriving trees from instances of the proxy principle. As a demonstration, we give a construction of a uniformly coherent κ-Souslin tree that applies also for κ inaccessible. We then carry out a systematic study of the consistency of instances of the proxy principle, distinguished by the vector of parameters serving as its input. Among other things, it will be shown that all known ⋄-based constructions of κ-Souslin trees may be redirected through this new proxy principle.

Original language	English
Pages (from-to)	1949-2007
Number of pages	59
Journal	Annals of Pure and Applied Logic
Volume	168
Issue number	11
DOIs	https://doi.org/10.1016/j.apal.2017.05.003
State	Published - Nov 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Funding

This work was partially supported by German-Israeli Foundation for Scientific Research and Development, Grant No. I-2354-304.6/2014. Some of the results of this paper were announced by the second author at the P.O.I. Workshop in pure and descriptive set theory, Torino, September 2015, and by the first author at the 8th Young Set Theory Workshop, Jerusalem, October 2015. The authors thank the organizers of the corresponding meetings for providing a joyful and stimulating environment. This work was partially supported by German-Israeli Foundation for Scientific Research and Development , Grant No. I-2354-304.6/2014 . Some of the results of this paper were announced by the second author at the P.O.I. Workshop in pure and descriptive set theory , Torino, September 2015, and by the first author at the 8th Young Set Theory Workshop , Jerusalem, October 2015. The authors thank the organizers of the corresponding meetings for providing a joyful and stimulating environment. We also thank the anonymous referee for his/her feedback.

Funders	Funder number
German-Israeli Foundation for Scientific Research and Development	I-2354-304.6/2014

Keywords

Coherence relation
Microscopic approach
Parameterized proxy principle
Regressive tree
Square principle
Uniformly coherent Souslin tree

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10.1016/j.apal.2017.05.003

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A microscopic approach to Souslin-tree constructions, Part I

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Keywords

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