Sketches the basic idea for the approach taken. A mathematical system is to be developed in which the existential theorems of traditional mathematics are to be replaced by constructibility theorems: where, in traditional mathematics, it is asserted that such and such exists, it will be asserted in this system that something or other can be constructed. Thus, constructibility quantifiers are introduced in this chapter as logical constants of formal systems. The logic of the constructibility quantifier is explained in each case via possible worlds semantics, which is used as a didactic or heuristic device.
Keywords: constructibility quantifier, mathematical existence, possible worlds semantics