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Published online by Cambridge University Press:  17 April 2014



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.

Copyright © Association for Symbolic Logic 2014 

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