WESSELS considered in [8] cut elimination in a Gentzen-style &-calculus without equality. But MINC pointed out in [6] that the proof in [8] is defective and mentions that the cut elimination theorem in a modified system can be proved model-theoretically. The work in 3 1, perhaps, carries out exactly
Cut Elimination in Transfinite Type Theory
β Scribed by Kenneth A. Bowen
- Publisher
- John Wiley and Sons
- Year
- 1973
- Tongue
- English
- Weight
- 953 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
I n an earlier paper [2], using ZERMELO-FRAENXEL set theory (ZF) as metalanguage, for each ordinal 6 2 1, I introduced a system TTo of transfinite type theory formulated in GENTZEN'S sequentzen style [3]. The notion of sequent and the rules of inference were straightforward generalizations of those
As SCOTT has shown, the Replacement. scheme of Z F derives a large part, of its strength from the Extensionality axiom. For in the absence of the latter, the supply of demonstrably functional formula matrices is relatively ineagei..l) I n this situation, u-e can restore some of Replacemmt's vigor by