Ideas from 'Constructibility and Mathematical Existence' by Charles Chihara [1990], by Theme Structure

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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
We could talk of open sentences, instead of sets [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Chihara's system is a variant of type theory, from which he can translate sentences [Shapiro]
We can replace type theory with open sentences and a constructibility quantifier [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Shapiro]