2,023 research outputs found
Separating Bounded Arithmetics by Herbrand Consistency
The problem of separating the hierarchy of bounded arithmetic has
been studied in the paper. It is shown that the notion of Herbrand Consistency,
in its full generality, cannot separate the theory from ; though it can
separate from . This extends a
result of L. A. Ko{\l}odziejczyk (2006), by showing the unprovability of the
Herbrand Consistency of in the theory .Comment: Published by Oxford University Press. arXiv admin note: text overlap
with arXiv:1005.265
A new coinductive confluence proof for infinitary lambda calculus
We present a new and formal coinductive proof of confluence and normalisation
of B\"ohm reduction in infinitary lambda calculus. The proof is simpler than
previous proofs of this result. The technique of the proof is new, i.e., it is
not merely a coinductive reformulation of any earlier proofs. We formalised the
proof in the Coq proof assistant.Comment: arXiv admin note: text overlap with arXiv:1501.0435
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