Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 23 min ago
PreprintCC BY 4.0arXiv

Closed maximal eventually different families for Σ03 and weakly Farah ideals

  • Jialiang He
  • Jiaheng Zhuang
  • Yi Zhou
Open at sourcePDFDOICite

Abstract

Motivated by the existence of closed maximal ℐ-eventually different (ℐ-MED) families, we study uniform combinatorial properties of ideals. For a fixed ideal, a property is uniform if its witnesses can be chosen by a single Borel map. We prove that every Σ03 ideal is uniformly weakly P+. We also prove that the classes of Farah and weakly Farah ideals coincide, answering a question of Hrušák and Meza-Alcántara. We then show that every weakly Farah ideal is uniformly weakly Ramsey. As an application, we obtain closed ℐ-MED families for Σ03 ideals and weakly Farah ideals.

Related

  1. A higher-dimensional Schrödinger maximal estimate along families of bi-Lipschitz curves
    Javier Minguillón
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Entropy bounds and global couplings for union-closed families
    Yunjiang Jiang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  3. Domination and maximal intersecting families in comaximal graphs of commutative rings
    Elham Mehdi-Nezhad
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Large Maximal Intersecting Families with Covering Number Three
    Huajun Zhang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. Metrization of the Fell Topology and the Wijsman Topology for the Box Metric on Closed Downward Families
    Shigeaki Yokota
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{he2026closed,
  title = {{Closed maximal eventually different families for $\boldsymbolΣ^0_3$ and weakly Farah ideals}},
  author = {Jialiang He and Jiaheng Zhuang and Yi Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28275},
  eprint = {2610.28275},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28275},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Closed maximal eventually different families for Σ^0_3 and weakly Farah ideals
AU  - Jialiang He
AU  - Jiaheng Zhuang
AU  - Yi Zhou
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28275
UR  - https://arxiv.org/abs/2610.28275
AB  - Motivated by the existence of closed maximal ℐ-eventually different (ℐ-MED) families, we study uniform combinatorial properties of ideals. For a fixed ideal, a property is uniform if its witnesses can be chosen by a single Borel map. We prove that every Σ^0_3 ideal is uniformly weakly P^+. We also prove that the classes of Farah and weakly Farah ideals coincide, answering a question of Hrušák and Meza-Alcántara. We then show that every weakly Farah ideal is uniformly weakly Ramsey. As an application, we obtain closed ℐ-MED families for Σ^0_3 ideals and weakly Farah ideals.
ER  -