We consider the positive set theory "Strong Frege 3" (SF3) proposed by E. W
eydert and discussed in [5]. SF3 is a "three valued" set theory where two b
inary predicates appear, is an element of and <(is an element of)over bar>,
mutually exclusive, but none of whom is the negation of the other (so give
n the sets x and y there are three possibilities: either x is an element of
y holds, or x<(is an element of)over bar>y holds, or both fail). SF3 gives
the axiom of extensionality with respect to is an element of and <(is an e
lement of)over bar>, and a comprehension scheme for those first order formu
las which are built positively from x is an element of y, x<(is an element
of)over bar>y, x = y and -(x = y)
In this paper we build a model M, which we conjecture to satiefy SF3, and v
ie prove that M does satisfy SF3 but in the logic without Leibniz rules for
equality; M is nontrivial in the sense that its equality relation is not t
he trivial relation which identifies everything. The construction uses an a
d hoc calculus c Delta(3), which is a typed, three-valued variant of the Fi
tch combinatory logic C Delta (see [1]).