[FOM] Query: references on intuitionistic Euclidean geometry
Vaughan Pratt
pratt at cs.stanford.edu
Thu Nov 19 17:35:33 EST 2009
Giovanni Sambin wrote:
> a student of mine plans to write a thesis on Euclidean geometry
developed over
> intuitionistic logic. I would appreciate any reference to books,
papers, or any other source on this topic.
Apropos of this question, the equational theory of vector spaces over a
fixed field can be axiomatized as a single-sorted theory having one
unary operation for each element of the field, along with the language
of groups. While I understand the concept of intuitionistic logic as a
first order logic, I don't know how it applies to an equationally
axiomatized theory. Is linear algebra when defined in this way
considered a classical theory, an intuitionistic one, both, or neither?
This is of course not Euclidean geometry but affine (and with an origin
but that's easily removed without leaving equational logic). However
the answer to the question for linear algebra (and hence affine
geometry) might serve as a useful point of comparison for any answer to
the corresponding question for Euclidean geometry.
Vaughan Pratt
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