Splitting and reaping numbers in shattered Cohen or Hechler iterations
Splitting and reaping numbers in shattered Cohen or Hechler iterations
Let and denote the splitting and reaping numbers, and let denote the continuum. Consider models obtained by the shattered iteration of either Cohen or Hechler forcing. Splitting–reaping conjecture. In these models,
For the corresponding shattered Mathias iteration, the theorem computes these characteristics at the iteration parameters, whereas for the Cohen and Hechler models only the bounds and are known. The conjecture is motivated by preservation of under finite-support iterations of Suslin ccc forcing over models of CH, but remains open.
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Sources & referencesView supporting material
Primary source
Joerg Brendle, “Shattered Iterations”, arXiv:2302.05069 (2023).
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