Year: 2026
Type: preprint
Abstract: We introduce d-minimal and b-minimal extensions, two weakenings of minimality based respectively on eventual domination and infinitely often domination. We prove that the generic extensions obtained by the full Mathias forcing and by Mathias forcing relative to Ramsey ultrafilters are d-minimal, whereas Hechler extensions are b-minimal. We also construct a d-minimal extension that is weakly $ω^ω$-bounding but neither minimal nor $ω^ω$-bounding, and realize every constellation of these properties compatible with their natural implications.
Source: arXiv (Cornell University)
Authors: Goldstern, Martin, Goto, Tatsuya
Institution: TU Wien
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213414987
Cites:
Cited by:
Related to: