Graduate studies at Western
Notre Dame Journal of Formal Logic 36 (2):185-213 (1995)
|Abstract||This paper is concerned with the interaction between formal semantics and the foundations of mathematics. We introduce a formal theory of truth, TLR, which extends the classical first order theory of pure combinators with a primitive truth predicate and a family of truth approximations, indexed by a directed partial ordering. TLR naturally works as a theory of partial classifications, in which type-free comprehension coexists with functional abstraction. TLR provides an inner model for a well known subsystem of second order arithmetic; indeed, TLR is proof-theoretically equivalent to Predicative Analysis|
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