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PreprintCC BY 4.0arXiv

Uncountably many maximally consistent neighborhood complete congruential modal logics

  • Zalán Gyenis
  • Krzysztof Krawczyk
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Abstract

We solve an open problem posed by Peter Fritz in \cite{Fritz} by proving that there are uncountably many C-Post complete congruential modal logics which are neighborhood complete. The method is algebraic: we construct an uncountable sequence of varieties of modal algebras which are minimal in the lattice of all subvarieties of modal algebras and are generated by a single complete and atomic modal algebra.

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Cite

BibTeXRIS
BibTeX
@misc{gyenis2026uncountably,
  title = {{Uncountably many maximally consistent neighborhood complete congruential modal logics}},
  author = {Zalán Gyenis and Krzysztof Krawczyk},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04508},
  eprint = {2609.04508},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04508},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Uncountably many maximally consistent neighborhood complete congruential modal logics
AU  - Zalán Gyenis
AU  - Krzysztof Krawczyk
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04508
UR  - https://arxiv.org/abs/2609.04508
AB  - We solve an open problem posed by Peter Fritz in \cite{Fritz} by proving that there are uncountably many C-Post complete congruential modal logics which are neighborhood complete. The method is algebraic: we construct an uncountable sequence of varieties of modal algebras which are minimal in the lattice of all subvarieties of modal algebras and are generated by a single complete and atomic modal algebra.
ER  -