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This paper is dedicated to my longtime friend and colleague Roel de Vrijer on the occasion of his sixtieth birthday. With its subject I have tried to go a little in his direction by taking a very syntactic subject. The work is part of a project in progress in cooperation with Rosalie Iemhoff and Nick Vaporis. It concerns the disjunction property in(More)
Proof terms in term rewriting are a representation means for reduction sequences, and more in general for contraction activity, allowing to distinguish e.g. simultaneous from sequential reduction. Proof terms for finitary, first-order, left-linear term rewriting are described in [15], ch. 8. In a previous work [12] we defined an extension of the finitary(More)
Barendregt's Lemma in its original form is a statement on Combinatory Logic that holds also for the lambda calculus and gives important insight into the syntactic interplay between substitution and reduction. Its origin lies in undefinablity proofs, but there are other applications as well. It is connected to the so-called Square Brackets Lemma, introduced(More)
One of the main foundations for this work is the theory of countable ordinals; (citation needed) and (citation needed) are good references on this subject. We want to point out some definitions and results which are critical in order to prove some of the basic properties of infinitary proof terms. In order to deal with infinitary composition, we will need(More)
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