Preservation of cardinal characteristics in shattered Cohen iterations
Preservation of cardinal characteristics in shattered Cohen iterations
Let , , and denote the bounding number, dominating number, and continuum, respectively. Assume
and let be regular cardinals with . Consider the extension by the shattered iteration of Cohen forcing. Preservation conjecture. In this extension,
and
The preceding results establish analogous preservation for the null ideal, while the authors state that they believe the corresponding values for the meager ideal and the bounding and dominating numbers are preserved but cannot prove it. The conjecture is open.
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Sources & referencesView supporting material
Primary source
Joerg Brendle, “Shattered Iterations”, arXiv:2302.05069 (2023).
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