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Oracle-Tree Forcing and Wilfs Inequality for Thirteen Left Elements — arXiv:2609.32078

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.32078
License (as archived): CC0-1.0
Archived: 2026-10-07T23:47:18.181Z
SHA-256 of the archived text: e6dbc7ab66d132f76ff2c15b13ed8b772cd37adba42fa069c0bcace8eac7b1b5
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How to cite

Oracle-Tree Forcing and Wilfs Inequality for Thirteen Left Elements — arXiv:2609.32078 — arXiv (en), https://arxiv.org/abs/2609.32078 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eaefba779c5d (Metraipolis archive dc_eaefba779c5d, sha256 e6dbc7ab66d132f76ff2c15b13ed8b772cd37adba42fa069c0bcace8eac7b1b5)

BibTeX

@misc{dceaefba779c5d,
  title = {Oracle-Tree Forcing and Wilfs Inequality for Thirteen Left Elements — arXiv:2609.32078},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.32078},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eaefba779c5d; sha256 e6dbc7ab66d132f76ff2c15b13ed8b772cd37adba42fa069c0bcace8eac7b1b5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.32078. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study filter-Laver forcing on omegaxomega with successor sets containing final quadrants. The observation retaining the minimum coordinate and orientation is a complete projection. Its finite nontrivial hidden-label quotients are Cohen, whereas the full offset quotient has Boolean density equal to the ground-model dominating number dV . For the associated grid-meager ideal I_box, we prove cov(I_box) = add(M) for the usual meager ideal M, and obtain further cardinal bounds. We also analyze threshold games, oracle degrees and the distinction between positive and filter-large certificate sets: recurrent filter-large acceptance admits refinements whose every branch succeeds. As an arithmetic application, we prove Wilfs inequality c \leq 13e for numerical semigroups with thirteen elements below the conductor c, where eis the embedding dimension. A complete arithmetic proof, including a bounded exact computation, is given in the appendix. Its terminating certificate procedures supply a computable quadrant tree and uniform refinements for every forcing condition. Finite support kernels describe persistence of the registered proofs; arithmetic absoluteness explains precisely why forcing organizes these certificates without replacing their arithmetic justification.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-29 in math.LO).
Categorie arXiv: Logic (math.LO).
Pagina del lavoro: https://arxiv.org/abs/2609.32078 — 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 2026-10-07T23:26:18.466Z dalla pagina https://arxiv.org/catchup/math.LO/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).