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СЕМИНАРЫ |
Семинары отдела математической логики "Теория доказательств" и "Logic Online Seminar"
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Provable well-orders and hyperarithmetical soundness D. Fernández-Duque Universitat de Barcelona |
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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 |