Geodesic
Joyal's arithmetic universe as list-arithmetic pretopos
Theory and applications of categories, Tome 24 (2010), pp. 39-83.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We explain in detail why the notion of list-arithmetic pretopos should be taken as the general categorical definition for the construction of arithmetic universes introduced by André Joyal to give a categorical proof of Gödel's incompleteness results.
Classification : 03G30, 03B15, 18C50, 03B20, 03F55
Keywords: Pretopoi, dependent type theory, categorical logic 
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     author = {Maria Emilia Maietti},
     title = {Joyal's arithmetic universe as list-arithmetic pretopos},
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     publisher = {mathdoc},
     volume = {24},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_24_a2/}
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Maria Emilia Maietti. Joyal's arithmetic universe as list-arithmetic pretopos. Theory and applications of categories, Tome 24 (2010), pp. 39-83. http://geodesic.mathdoc.fr/item/TAC_2010_24_a2/