1995
DOI: 10.1016/0168-0072(94)00056-9
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Proof-theoretic analysis of termination proofs

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Cited by 38 publications
(46 citation statements)
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“…Here is a proof of of the wellfoundedness property (4), taken from on Buchholz [2]. (We generalized it slightly from the one-sorted to the many-sorted setting and from the assumption that < is a finite linear order on Σ to the assumption that < is any wellfounded order.…”
Section: < Is Monotonic (It Has Thementioning
confidence: 99%
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“…Here is a proof of of the wellfoundedness property (4), taken from on Buchholz [2]. (We generalized it slightly from the one-sorted to the many-sorted setting and from the assumption that < is a finite linear order on Σ to the assumption that < is any wellfounded order.…”
Section: < Is Monotonic (It Has Thementioning
confidence: 99%
“…For part (1), note that if [α]P * C ψ is a normal form, then each sentence P A [β]P * C ψ and all subsentences of this sentence are normal forms. For part (2), note that when ϕ is a normal form, ϕ ∈ f (ϕ).…”
Section: (δ) and Nf ([δ]χ)mentioning
confidence: 99%
“…However, because these results rely on proving termination of term rewriting systems, they cannot be scaled to arithmetic (by Gödel's second incompleteness theorem and [Buc95]). …”
Section: Resultsmentioning
confidence: 99%
“…The subterm, monotonicity and transitivity properties are shown in [KL80], well-foundedness is shown in [Buc95]. The big head property can be shown by a straightforward induction on the structure of t.…”
Section: The Lexicographic Path Orderingmentioning
confidence: 99%
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