2 results
COMPACT CARDINALS AND EIGHT VALUES IN CICHOŃ’S DIAGRAM
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- Journal:
- The Journal of Symbolic Logic / Volume 83 / Issue 2 / June 2018
- Published online by Cambridge University Press:
- 01 August 2018, pp. 790-803
- Print publication:
- June 2018
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- Article
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Assuming three strongly compact cardinals, it is consistent that
$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) < \mathfrakb < \mathfrakd < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$Under the same assumption, it is consistent that
$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) < non\left( {\cal M} \right) < cov\left( {\cal M} \right) < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$
COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS
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- Journal:
- The Journal of Symbolic Logic / Volume 83 / Issue 1 / March 2018
- Published online by Cambridge University Press:
- 05 February 2018, pp. 208-236
- Print publication:
- March 2018
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- Article
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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.
