Re: "classical" computability theory and the category of Sets

[Michael Barr <barr@math.mcgill.ca>]

A student of mine, James R. Otto worked on this for his thesis.
Unfortunately, it was famously unreadable.  I don't think it was published
and I have lost contact with him.  It was in the early 90s.

Michael

On Wed, 2 Jul 2014, Vasili I. Galchin wrote:

> Hello Cat Theory list,
>
>     Please be gentle.
>
>     In the past I studied computability theory. It seems to me that
> this theory  is built on the category of Sets(elementary topos), i.e.
> this computability theory assumes using classical logic with LEM and
> boolean subobject classifier for concepts like semi-decidability, etc.
> Is there a notion of intuitionistic computability theory built on
> other topoi where LEM is absent from the accompanying higher logic and
> the topos' subobject classifier has a internal Heyting algebra(that is
> not boolean)?? Is this what realizibility delves into(I have yet to
> study realizibility concepts).
>
> Kind regards,
>
> Vasya
>
>

-- 
         Every gun that is made, every warship launched, every rocket fired
signifies, in the final sense, a theft from those who hunger and are not
fed, those who are cold and are not clothed. -Dwight D. Eisenhower



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