Dear Bill, > The only thing missing here is the concept of sub-object (sub-domain) > and how it should interact with logic, otherwise the underlying structure of > the > language would essentially be a topos (algebraic set theory). And a > lot (maybe almost all of mathematics or at least the constructive part > of mathematics?) can be done as internal structures of such a > mathematical category.
Hm, can you make that statement more precise? [I am much interested still in this issue] I would like to warn you that `topos valid' mathematics is probably not what people in computer algebra (or Bishop) would call 'constructive'. While the logic is weaker, it still has some sort of existential quantifyer, which allows you to state existence without being able to 'generate' such an object. Such a situation, many people would call non-constructive. There are quite a few mathematicians which do not see a topos as a sort of set theory, but look at them much more as a theory of spaces. Also I guess your topos is an elementary topos not a Grothendieck topos?. Cheers BF. -- % PD Dr Bertfried Fauser % Research Fellow, School of Computer Science, Univ. of Birmingham % Privat Docent: University of Konstanz, Physics Dept <http://www.uni-konstanz.de> % contact |-> URL : http://www.cs.bham.ac.uk/~fauserb/ % Phone : +44-121-41-42795 -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
