Andrej Bauer on Intuitionistic Logic and Constructive Mathematics

13:42 A modality is a Monad on Propositions (and the theory of a monad is decidable! See Oracle modalities by Andrew W Swan and Andrej Bauer and Ronald Brown On Monads and Groupoids and Alexander Grothendieck on his idea for a Science Fiction Novel on Motives).

To understand this idea you need to be able to understand Kleene's notion of Realizability and Hyland's Effective Topos which depends heavily upon Tripos Theory, a tripos here is "a topos-representing, indexed, pre-ordered set".  Kleene's attempts to interpret intuitionistic logic were all more than a little weird, I suspect he had dubious motives. See Markov's principle and Realizability.  Intuitionistic logic is in a sense strictly more expressive than classical logic. See Emily Riehl on Univalent Foundations.

Subscribe to Types and Topology Workshop.

Dr. Martin Escardo on Searchable sets and ordinals in system T given at a six month 2012 programme called Semantics and syntax: a legacy of Alan Turing:


Subscribe to INI Seminar Room 1.

I have been finding more and more interesting things people have written on coalgebraic types and totality:

See Mark Jago on Type Theory in Computer Science, Logic and Linguistics.

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