Cut-Simulation and Impredicativity

Details Cut-Simulation and Impredicativity Cut-Simulation and Impredicativity

2009-01-31

arxiv.org/abs/0902.0043v2

Computer Science

Logic in Computer Science

21 pages

Scientific paper

We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type theory -- is like adding cut. The phenomenon equally applies to prominent axioms like Boolean- and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.

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