Poésie Aristotélienne

Shimon Garti; Saharon Shelah

doi:10.36045/j.bbms.240523

Poésie Aristotélienne

Shimon Garti, Saharon Shelah

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the exact consistency strength of (^ω_ω²₁) → (_ωⁿ₁)_ω for every n ∈ ω with (^ω_ω²₁) 9 (_ω^ω₁)_ω is an ω₁-Erdős cardinal. We also prove that if κ is strongly inaccessible then (^κ_κ⁺) → (_κ²)_<κ implies (^κ_κ⁺) → (^γ_κ)_<κ for every γ ∈ κ.

Original language	French
Pages (from-to)	67-74
Number of pages	8
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	32
Issue number	1
DOIs	https://doi.org/10.36045/j.bbms.240523
State	Published - 1 Apr 2025

Keywords

Aristotelian poetry
Erdős cardinals
Polarized partition relations

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.36045/j.bbms.240523

Cite this

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abstract = "We prove that the exact consistency strength of (ωω21) → (ωn1)ω for every n ∈ ω with (ωω21) 9 (ωω1)ω is an ω1-Erd{\H o}s cardinal. We also prove that if κ is strongly inaccessible then (κκ+) → (κ2)<κ implies (κκ+) → (γκ)<κ for every γ ∈ κ.",

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AB - We prove that the exact consistency strength of (ωω21) → (ωn1)ω for every n ∈ ω with (ωω21) 9 (ωω1)ω is an ω1-Erdős cardinal. We also prove that if κ is strongly inaccessible then (κκ+) → (κ2)<κ implies (κκ+) → (γκ)<κ for every γ ∈ κ.

KW - Aristotelian poetry

KW - Erdős cardinals

KW - Polarized partition relations

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DO - 10.36045/j.bbms.240523

M3 - مقالة

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JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

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Poésie Aristotélienne

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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