"** new foundations must give new math**"

from

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 »
Taylor

**Paul Taylor**

London

**Equideductive logic**

In any category with products, equalisers and powers of a base object,
the regular monos (those than can be expressed as equalisers) admit
intersections and a universal quantifier of the form

q(x) === All y. \p(y) ==> f x y = g x y

Although this is a very feeble logic, it is interesting because

- it is enough to state judgements and proof rules in algebra,
- some forms of induction can be written in it,
- it fits together very neatly with the lattice structure and especially the Euclidean principle in ASD, and
- it is enough to reproduce a construction similar to that of Scott's equilogical spaces.

The modified equilogical space construction does not have all of the
properties that one would like from either ASD or functional analysis.

However, since equideductive logic is so simple, it should be easy to
show that axioms can be added to it conservativity, although this is
a point on which I would find advice from proof theorists very useful.

Please see the final section of my paper "**Foundations for
Computable Topology**" for more details: www.PaulTaylor.EU/ASD/foufct/