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Семинары отдела математической логики "Теория доказательств" и "Logic Online Seminar"
21 мая 2024 г. 18:30, г. Москва, МИАН (ул. Губкина, 8), ауд. 313 + Zoom


Provable well-orders and hyperarithmetical soundness

D. Fernández-Duque

Universitat de Barcelona



Аннотация: Joint work with Juan Aguilera
Ordinal analysis traditionally measures the strength of formal theories using the supremum of the order types of their provable well-orders. In this talk, we will instead propose the use of proof-theoretic ordinals to measure de degree of soundness of a theory: to be precise, we define an ordinal-theoretic measure of the degree of hyperarithmetical correctness of a mathematical theory. We then characterize the ordinals that are assigned in this way to theories of various degrees of hyperarithmetical soundness.

Язык доклада: английский


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