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COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS

Published online by Cambridge University Press:  05 February 2018

VERA FISCHER ,
SY D. FRIEDMAN ,
DIEGO A. MEJÍA  and
DIANA C. MONTOYA
VERA FISCHER
Affiliation:
KURT GÖDEL RESEARCH CENTER UNIVERSITY OF VIENNA WÄHRINGER STRASSE 25 1090 VIENNA, AUSTRIA E-mail:vera.fischer@univie.ac.atURL: http://www.logic.univie.ac.at/∼vfischer/
SY D. FRIEDMAN
Affiliation:
KURT GÖDEL RESEARCH CENTER UNIVERSITY OF VIENNA WÄHRINGER STRASSE 25 1090 VIENNA, AUSTRIA E-mail:sdf@univie.ac.atURL: http://www.logic.univie.ac.at/∼sdf/
DIEGO A. MEJÍA
Affiliation:
CREATIVE SCIENCE COURSE (MATHEMATICS) FACULTY OF SCIENCE, SHIZUOKA UNIVERSITY, OHYA 836, SURUGA-KU SHIZUOKA-SHI, 422-8529, JAPAN E-mail:diego.mejia@shizuoka.ac.jpURL: http://www.researchgate.com/profile/diego_mejia2
DIANA C. MONTOYA
Affiliation:
KURT GÖDEL RESEARCH CENTER UNIVERSITY OF VIENNA WÄHRINGER STRASSE 25 1090 VIENNA, AUSTRIA E-mail:dcmontoyaa@gmail.comURL: http://www.logic.univie.ac.at/∼montoyd8/
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Abstract

We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations in Cichoń’s diagram, in particular, a model where the diagram can be separated into 7 different values. Furthermore, we show that this constellation of 7 values is consistent with the existence of a ${\rm{\Delta }}_3^1$ well-order of the reals.

Keywords

03E1703E1503E3503E4003E45Cichoń’s diagramfinite support iterations3D-coherent systems2D-coherent systemsΔ31 well-orders
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 208 - 236
Copyright
Copyright © The Association for Symbolic Logic 2018 

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