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A NEW COMPUTATION OF THE Σ-ORDINAL OF KPω
Published online by Cambridge University Press: 17 April 2014
Abstract
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 Δ1-comprehension and strict-${\rm{\Pi }}_1^1$ reflection and show that the Σ-ordinal of this theory is still the Bachmann-Howard ordinal. It is also argued that the second-order theory is Σ1-conservative over KPω.
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- Copyright © Association for Symbolic Logic 2014
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