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Seminars "Proof Theory" and "Logic Online Seminar"
May 21, 2024 18:30, Moscow, Steklov Mathematical Institute (8 Gubkina), room 313 + Zoom
 


Provable well-orders and hyperarithmetical soundness

D. Fernández-Duque

Universitat de Barcelona
Video records:
MP4 743.9 Mb
MP4 509.3 Mb

Number of views:
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Video files:42



Abstract: 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.

Language: English
 
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