From this you can draw the conclusion that a preserves the validity of
While writing a joint paper with Steve Awodey, we came to think about the following question: Given a Grothendieck topos Sh(C), what logic is preserved by the associated sheaf functor from Sh(C) to the double negation subtopos of Sh(C)? We know that a: Sh(C) --> DNSh(C) preserves geometric logic. Since it is double negation it also preserves 0 (falsehood), negation and implication. formulas built up from double negation stable predicates without universal quantifiers. Presumably this has been studied in the literature, can something stronger be said about what validities are preserved, could anyone provide a reference for a general result of this kind? Grateful for any help, Jonas Eliasson ------------------------------------------ | Jonas Eliasson | | Department of Mathematics | | Uppsala University | | Sweden | | E-mail: jonase@math.uu.se | | Homepage: http://www.math.uu.se/~jonase/ | ------------------------------------------