Remarks on the foundations of mathematics

Treść dostarczona przez Ludwig-Maximilians-Universität München and MCMP Team. Cała zawartość podcastów, w tym odcinki, grafika i opisy podcastów, jest przesyłana i udostępniana bezpośrednio przez Ludwig-Maximilians-Universität München and MCMP Team lub jego partnera na platformie podcastów. Jeśli uważasz, że ktoś wykorzystuje Twoje dzieło chronione prawem autorskim bez Twojej zgody, możesz postępować zgodnie z procedurą opisaną tutaj https://pl.player.fm/legal.

MCMP – Philosophy of Mathematics «
Remarks on the foundations of mathematics

10+ y ago 1:31:37

Udostępnij

MP4

Fetch error

Hmmm there seems to be a problem fetching this series right now. Last successful fetch was on October 13, 2022 23:55 (2y ago)

What now? This series will be checked again in the next day. If you believe it should be working, please verify the publisher's feed link below is valid and includes actual episode links. You can contact support to request the feed be immediately fetched.

Helmut Schwichtenberg (LMU) gives a talk at the MCMP Colloquium (5 December, 2013) titled "Remarks on the foundations of mathematics". Abstract: We consider minimal logic with implication and universal quantification over (typed) object variables. Free type and predicate parameters may occur. For mathematics we need (i) data (the Scott - Ershov partial continuous functionals) and (ii) predicates (defined inductively or coinductively). In this setting we can define (Leibniz) equality, falsity and the missing logical connectives (negation, disjunction, existential quantification, conjunction). Ex-falso-quodlibet can be proved. Using Kreisel's (modified) realizability we can (even practically) extract computational content from proofs, and (internally) prove soundness.

22 odcinków

#Germany #LudwigMaximiliansUniversität München Is One #MCMP Team #Philosophy #Logic #Science #Language #Mathematics #Hannes Leitgeb #Stephan Hartmann #Alexander Von Humboldt Foundation #Munich Center For Mathematical Philosophy #MCMP #LMU