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SQUARE WITH BUILT-IN DIAMOND-PLUS

Published online by Cambridge University Press:  08 September 2017

ASSAF RINOT  and
RALF SCHINDLER
ASSAF RINOT
Affiliation:
DEPARTMENT OF MATHEMATICS BAR-ILAN UNIVERSITY RAMAT-GAN52900, ISRAELE-mail: [email protected]: http://www.assafrinot.com
RALF SCHINDLER
Affiliation:
INSTITUT FÜR MATHEMATISCHE LOGIK UND GRUNDLAGENFORSCHUNG UNIVERSITÄT MÜNSTER, EINSTEINSTR. 62 48149 MÜNSTER, GERMANYE-mail: [email protected]: http://www.math.uni-muenster.de/logik/personen/rds
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Abstract

We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds in L for every infinite cardinal.

As an application, we prove that the following two hold in L:

  1. 1. For every infinite regular cardinal λ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;

  2. 2. For every infinite cardinal λ, there exists a respecting λ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed in L.

Keywords

Primary 03E45Secondary 03E05diamond principlesquare principleconstructibilitywalks on ordinalsKurepa treealmost Souslin treeparameterized proxy principle
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 3 , September 2017 , pp. 809 - 833
Copyright
Copyright © The Association for Symbolic Logic 2017 

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