# COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS

@article{Fischer2018COHERENTSO,
title={COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS},
author={Vera Fischer and Sy-David Friedman and Diego Alejandro Mej{\'i}a and Diana Carolina Montoya},
journal={The Journal of Symbolic Logic},
year={2018},
volume={83},
pages={208 - 236}
}
• Published 18 September 2016
• Physics, Computer Science
• The Journal of Symbolic Logic
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.
15 Citations

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