Van Douwen and Many Non Van Douwen Families
Year: 2026
Type: article
Abstract: We prove that the spectrum of Van Douwen families is closed under singular limits. For any maximal eventually different family Raghavan defined in [10] an associated ideal which measures how far the family is from being Van Douwen. Under CH we prove that every ideal containing $\mathrm {Fin}$ is realized as the associated ideal of some maximal eventually different family. Finally, we construct maximal eventually different families with Sacks-indestructible associated ideals to prove that in the iterated Sacks-model every $\aleph _1$ -generated ideal containing $\text {Fin}$ is realized.
Source: Journal of Symbolic Logic
Author: LUKAS SCHEMBECKER
Institution: Universität Hamburg
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4416013607
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