David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Topoi 3 (1):13-22 (1984)
The purpose of this paper is to justify the claim that Topos theory and Logic (the latter interpreted in a wide enough sense to include Model theory and Set theory) may interact to the advantage of both fields. Once the necessity of utilizing toposes (other than the topos of Sets) becomes apparent, workers in Topos theory try to make this task as easy as possible by employing a variety of methods which, in the last instance, find their justification in metatheorems from Logic. Some concrete instances of this assertion will be given in the form of simple proofs that certain theorems of Algebra hold in any (Grothendieck) topos, in order to illustrate the various techniques that are used. In the other direction, Topos theory can also be a useful tool in Logic. Examples of this are independence proofs in (classical as well as intuitionistic) Set theory, as well as transfer methods in the presence of a sheaf representation theorem, the latter applied, in particular, to model theoretic properties of certain theories.
|Keywords||Topos Theory Logic Model Theory Set Theory|
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References found in this work BETA
R. I. Goldblatt (2006). Topoi: The Catergorical Analysis of Logic. Dover Publications.
André Boileau & André Joyal (1981). La Logique Des Topos. Journal of Symbolic Logic 46 (1):6-16.
M. P. Fourman, D. S. Scott & C. J. Mulvey (1983). Sheaves and Logic. Journal of Symbolic Logic 48 (4):1201-1203.
R. J. Grayson (1982). Concepts of General Topology in Constructive Mathematics and in Sheaves, II. Annals of Mathematical Logic 23 (1):55-98.
Anders Kock & Gonzalo E. Reyes (1977). Doctrines in Categorical Logic. In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co. 90.
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