The classical topological model for intuitionistic predicate logic was extended by SCOTT [Ti] and J. R. MOSCHOVAKIS [3] to intuitionistic analysis. This intuitionistic analysis includes a strong version of Kripke's schema and is thus different from TROELSTRA's system C s [6]. I n this paper we will describe a variant of our model for intuitionistic set-theory [4] that will be a model for CS. It will be similar to the Scott-Moschovakis model but have another topology. We do not aspire any similarity to TROELSTRA'S intuitionistic models as presented in [6, Appendix C]. So i t is also with VAN DALEN'S intuitionistic analysis [l], his interpretation is not a topological one but can itself be interpreted as a topological one. -The author thanks A. S. TROELSTRA and G. F. VAN DER HOEVEN, Amsterdam, for their valuable criticism of earlier drafts of this paper.
We begin by some notations and simple definitions for the "lau4ike" objects. They essentially copy TROELSTRA'S notions, as to make the lawlike part of CS valid. Let x, y, z, u , v, m, n be variables for classical natura,l numbers, a, b , c, d variables for classical sequences (elements of the Baire space A"'-), i , il. jz constants for a pairing function and its inverses, ?, the ?.-operator. So we have il(i(2, Y)) = 5 , (?,s.t(x)) t' = t(t') . iz(i(x3 Y)) = Y > i(il(4, i&)) = 2, Defining (b), : = ?,y.b(j(x, y)), the schema AC-NF Vx 3uH(x, a ) + 3b Vx(x, (b)r)