"new foundations must give new math"
from "The Basic Picture. Structures for constructive
topology"
by Giovanni Sambin, Oxford University Press, forthcoming
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Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Italy
University of Padova, Italy
AILA (Italian Association of Logic and Applications), whose first president was Giovanni Sambin (from 1987 to 1994).
Giuseppe Rosolini
Genova
Structuring models of quotients
(joint with Maria Emilia Maietti)
We present a unifying notion of categorical completion by quotients
which applies to coherent theories and models, and show that such
a construction decomposes into three "logical" steps: the first freely
expands the logic with comprehension, the second turns logical images
into images of functions but does not change the logic, the third
adds quotients.
The construction encompasses most of the models constructed in type
theory and in category theory such as the setoid model of Martin-Löf
Type Theory, toposes of sheaves and the effective topos.