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This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on Realisability [8] and the other on Sheaf Models in Algebraic Set Theory [9]. Sheaf theory and realisability have been effective methods for constructing models of various constructive and intuitionistic… (More)

1 Introduction This paper is the second in a series on the relation between algebraic set theory [19] and predicative formal systems. The purpose of the present paper is to show how realizability models of constructive set theories fit into the framework of algebraic set theory. It can be read independently from the first part [5]; however, we recommend… (More)

Introduction. This paper deals with locales and their spaces of points in intuitionistic analysis or, if you like, in (Grothendieck) toposes. One of the important aspects of the problem whether a certain locale has enough points is that it is directly related to the (constructive) completeness of a geometric theory. A useful exposition of this relationship… (More)