We define a functional interpretation of KPω using Howard’s primitive recursive tree functionals of finite type and associated terms. We prove that the Σ-ordinal of KPω is the least ordinal not given by a closed term of the ground type of the trees (the Bachmann-Howard ordinal). We also extend KPω to a second-order theory with ∆1-comprehension and strict-Π 1 1 reflection and show that the Σ-ord...

We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three axioms: separation monotonic, separation upper invariant, and separation lower invariant. Each axiom is a natural restriction on how mechanisms can react wh...

We show that that if every real has a sharp and there are 1 2-deenable prewellorderings of R of ordinal ranks unbounded in ! 2 , then there is an inner model for a strong cardinal. Similarly, assuming the same sharps, the Core Model K is 1 3-absolute unless there is an inner model for a strong cardinal.

Ordinal analysis is a research program wherein recursive ordinals are assigned to axiomatic theories. According conventional wisdom, ordinal measures the strength of Yet what attendant notion strength? In this paper we present abstract characterizations that address question. First, characterize as partition Σ11-definable and Π11-sound theories, namely, whereby two theories equivalent if they h...