"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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Under the patronage of

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).

Abstracts » Rosolini

Giuseppe Rosolini

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.