[Agda] Classical Mathematics for a Constructive World
Peter Divianszky
divipp at gmail.com
Wed Nov 28 01:02:18 CET 2012
On 27/11/2012 23:37, Martin Escardo wrote:
>>>> Isn't the latter more "classical"?
>>>
>>> What is a classical space?
>>
>> I would use the phrase "classical space" for a space (¬ ¬ A) for some A
>> and "classical function space" for a function space (B → ¬ ¬ A). What do
>> you think about it?
>
> Spaces of the form ¬¬X have at most one element.
What a pity.
I would try then
classical-space A
= Sigma (A -> Set) (\P -> ¬¬ Sigma A P)
classical-function-space A B
= classical-space (A -> B)
classical-sequence A
= classical-function-space Nat A
I have to read more and compare this definition to others.
Thanks,
Peter
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