TITLE: A Model where Dedekind Reals and Cauchy Reals are Different
QUESTION [30 upvotes]: Is there a model where Dedekind reals and Cauchy reals are different? I'd appreciate if someone can refer me to any related work in case such a model exists.

REPLY [2 votes]: A good reference for this is Fourman and Hyland's 1970 paper on sheaf models for analysis,

Fourman M.P., Hyland J.M.E. (1979) Sheaf models for analysis. In: Fourman M., Mulvey C., Scott D. (eds) Applications of Sheaves. Lecture Notes in Mathematics, vol 753, doi:10.1007/BFb0061823

which I managed to find online here:
https://www.dpmms.cam.ac.uk/~martin/Research/Oldpapers/analysis79.pdf