Narrow systems revisited

0586663 - MÚ 2025 RIV US eng J - Journal Article
Lambie-Hanson, Christopher
Narrow systems revisited.
Bulletin of the London Mathematical Society. Roč. 56, č. 6 (2024), s. 1967-1987. ISSN 0024-6093. E-ISSN 1469-2120
R&D Projects: GA ČR(CZ) GA23-04683S
Institutional support: RVO:67985840
Keywords : cardinal arithmetic * generalized narrow system * set-theoretic compactness principles
OECD category: Pure mathematics
Impact factor: 0.9, year: 2022
Method of publishing: Open access
https://doi.org/10.1112/blms.13037

We investigate connections between set-theoretic compactness principles and cardinal arithmetic, introducing and studying generalized narrow system properties as a way to approach two open questions about two-cardinal tree properties. The first of these questions asks whether the strong tree property at a regular cardinal (Formula presented.) implies the singular cardinals hypothesis ((Formula presented.)) above (Formula presented.). We show here that a certain narrow system property at (Formula presented.) that is closely related to the strong tree property, and holds in all known models thereof, suffices to imply (Formula presented.) above (Formula presented.). The second of these questions asks whether the strong tree property can consistently hold simultaneously at all regular cardinals (Formula presented.). We show here that the analogous question about the generalized narrow system property has a positive answer. We also highlight some connections between generalized narrow system properties and the existence of certain strongly unbounded subadditive colorings.
Permanent Link: https://hdl.handle.net/11104/0354096