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Logic Online Seminar (https://www.mathnet.ru/conf876)
Monday 16:00 MSK (UTC+3), Room 313 MIAN + Zoom (online talk)

02.12.2024 Wei Wang (Sun Yat-sen University, Guangzhou): Definable Combinatorial Principles in Fragments of Arithmetic (online only)

In fragments of arithmetic, the pigeonhole principle may fail for definable partitions of finite sets. Dimicoupolous and Paris proved that over IΣ_1 the ordinary pigeonhole principle for Σ_n+1 partitions is equivalent to BΣ_n+1 (n0). Later Kaye formulated several second order pigeonhole principles which are used to axiomatise κ-like models of arithmetic. A first order fragment derived from one of Kaye's pigeonhole principles, known as
Σ_n-cardinality scheme or CΣ_n, has interesting independence properties proved by Kaye himself and also proved useful in reverse mathematics. Recently, we study another first order fragment of these pigeonhole principles, called Generalised Pigeonhole Principle (GPHP) by Kaye. We shall introduce some progress concerning Σ_n+1-GPHP from perspectives of both first order arithmetic and reverse mathematics.

🔗 Семинары отдела математической логики "Теория доказательств" и "Logic Online Seminar&


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