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A Side Condition Principle With Applications — arXiv:2611.04362

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04362
License (as archived): CC0-1.0
Archived: 2026-11-04T19:02:43.725Z
SHA-256 of the archived text: ee6335430c6fd60e12a0a036c24cb2a19ab476addce2dc1653661c4cbf8561e5
Stable URL of this page: https://metraipolis.com/documento/dc_09596fddbf97

How to cite

A Side Condition Principle With Applications — arXiv:2611.04362 — arXiv (en), https://arxiv.org/abs/2611.04362 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_09596fddbf97 (Metraipolis archive dc_09596fddbf97, sha256 ee6335430c6fd60e12a0a036c24cb2a19ab476addce2dc1653661c4cbf8561e5)

BibTeX

@misc{dc09596fddbf97,
  title = {A Side Condition Principle With Applications — arXiv:2611.04362},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04362},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_09596fddbf97; sha256 ee6335430c6fd60e12a0a036c24cb2a19ab476addce2dc1653661c4cbf8561e5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04362. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We introduce a combinatorial principle $\textsf{SC}(\kappa)$, for any regular cardinal $\kappa \ge \omega_2$, which asserts the existence of a family $\mathcal{Y} \subseteq [H(\kappa)]^\omega$ of elementary substructures of $H(\kappa)$ which is closed under finite intersections and satisfies that for stationarily many $N \in \mathcal{Y}$, if $M \in \mathcal{Y}$ and $M \cap \omega_1 < N \cap \omega_1$, then $M \cap N \cap \kappa \in N$. We explore the idea of defining forcings with side conditions consisting of finite subsets of such a family $\mathcal{Y}$. If $\textsf{SC}(\omega_2)$ holds, then there exists a thin stationary subset of $[\omega_2]^\omega$, and consequently $\textsf{SC}(\omega_2)$ is independent of ZFC. Assuming that $\mu$ is a Mahlo cardinal, the Lévy collapse $\mathrm{Col}(\omega,<\mu)$ forces that $\textsf{SC}(\kappa)$ holds for all regular cardinals $\kappa \ge \omega_2$. Local instances of $\textsf{SC}$ can be forced using matrices of models or derived as consequences of square principles. We apply the principle $\textsf{SC}$ to define two kinds of forcings: a streamlined version of a strongly proper collapse, and a forcing which is strongly proper on a stationary set and adds arbitrarily many Baumgartner clubs. Finally, we prove two consistency results using forcings derived from $\textsf{SC}$ related to Aronszajn trees, the guessing model principle, strong failures of club guessing, and the higher dominating number.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.LO, nuovi lavori del giorno).
Categorie arXiv: Logic (math.LO).
Pagina del lavoro: https://arxiv.org/abs/2611.04362 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:38:52.365Z dalla pagina https://arxiv.org/list/math.LO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).