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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 20th 2015

stub for arithmetic pretopos, just to record the reference

• CommentRowNumber2.
• CommentAuthorDavidRoberts
• CommentTimeMay 21st 2015
• (edited May 21st 2015)

We have the grey link arithmetic universe at abstract Stone duality, which we may want to redirect to arithmetic pretopos. I only don’t do it, since these are not the same thing (an AU has been defined by Joyal, though no one has seen it), even though Maietti’s proposal is that an arithmetic universe be defined as a list-arithmetic pretopos.

I hope we can flush Joyal’s definition out of the undergrowth…

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 21st 2015

I have added to arithmetic pretopos the redirect and the sentence

Maietti proposed that arithmetic pretoposes serve as the arithmetic universes that Andre Joyal once suggested to use for discussion of incompleteness theorems.

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeMay 21st 2015

Alright :-). I guess there’s not much to discuss…

• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeMay 21st 2015
• (edited May 21st 2015)

Trying to unwind Maietti’s definition of parameterised list objects, I guess they are just W-types for the non-locally cartesian closed version of the polynomial functor giving list objects. Cockett (JPAA 1990) defines them as initial algebras for the endofunctor $B+A\times (-)$ (for arbitrary $A$ and $B$).

Let me edit that in now… (EDIT: done!)

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMay 21st 2015
• (edited May 21st 2015)

Thanks!

Gave hyperlinks to you finite products and (more importantly) disjoint coproducts.