A modern elaboration of the ramified theory of types

Studia Logica 57 (2-3):243 - 278 (1996)
Abstract
The paper first formalizes the ramified type theory as (informally) described in the Principia Mathematica [32]. This formalization is close to the ideas of the Principia, but also meets contemporary requirements on formality and accuracy, and therefore is a new supply to the known literature on the Principia (like [25], [19], [6] and [7]).As an alternative, notions from the ramified type theory are expressed in a lambda calculus style. This situates the type system of Russell and Whitehead in a modern setting. Both formalizations are inspired by current developments in research on type theory and typed lambda calculus; see [3].
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