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Combinatorics in 1-semi-equational theories — arXiv:2609.07475

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.07475
License (as archived): CC0-1.0
Archived: 2026-10-16T14:49:22.334Z
SHA-256 of the archived text: a84b3520905aea3d76f3b242ca6761637816ad7493102afa5aca5d6edfb5de75
Stable URL of this page: https://metraipolis.com/documento/dc_effbd21930dc

How to cite

Combinatorics in 1-semi-equational theories — arXiv:2609.07475 — arXiv (en), https://arxiv.org/abs/2609.07475 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_effbd21930dc (Metraipolis archive dc_effbd21930dc, sha256 a84b3520905aea3d76f3b242ca6761637816ad7493102afa5aca5d6edfb5de75)

BibTeX

@misc{dceffbd21930dc,
  title = {Combinatorics in 1-semi-equational theories — arXiv:2609.07475},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.07475},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_effbd21930dc; sha256 a84b3520905aea3d76f3b242ca6761637816ad7493102afa5aca5d6edfb5de75},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.07475. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We give direct combinatorial proofs that 1-semi-equational theories satisfy two combinatorial properties that imply the non-interpretability of certain fields. Our main result is that Boolean combinations of 1-semi-equations have almost linear Zarankiewicz bounds, and hence no infinite field is interpretable in a 1-semi-equational theory; this answers a question of Chernikov--Mennen and Chernikov--Starchenko, who had respectively established almost linear Zarankiewicz bounds for Boolean combinations of $(2,1)$-semi-equations and Boolean combinations of weakly normal relations. (This was recently and independently established by Gou, Mirabi, Mittal, Tran, and Yang, using different techniques and producing different bounds.) We also show that $(k,1)$-semi-equations satisfy the $\delta$-strong Erdős--Hajnal property with $\delta=1/6^{k-1}$; this had previously been established by Chernikov--Starchenko for an ineffective constant $\delta>0$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.CO).
Categorie arXiv: Logic (math.LO) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.07475 — 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 2026-10-16T14:32:29.931Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).