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Preprint Number 2192
2192. Pablo Andújar Guerrero Definable (ω, 2)-theorem for families with VC-codensity less than
2 E-mail: Submission date: 26 May 2022 Abstract: Let S be a family of sets with VC-codensity less than 2. We prove that, if S has the (ω, 2)-property (for any infinitely many sets in S, at least 2 among them intersect), then S can be partitioned into finitely many subfamilies, each with the finite intersection property. If S is definable in some first-order structure, then these subfamilies can be chosen definable too. This is a strengthening of the base case of the definable (p,q)-conjecture in model theory and of the Alon-Kleitman-Matoušek (p,q)-theorem in combinatorics. Mathematics Subject Classification: 03C45, 52A35 Keywords and phrases: |

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