G. Gentzen. Die Widerspruchsfreiheit der Stufenlogik. Mathematische Zeitschrift, 41.3:357--366, 1936. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On the meaning of logical rules I: syntax vs. semantics - Girard (1998) (Correct)
....w.r.t. games should be stated as follows : if oe is a winning strategy for the game jAj, then there is a proof of A such that oe = jj. By the way Gentzen is not only responsible for sequent calculus, but also for the game interpretation of logic: In his immature first consistency proof, [10, 11] of arithmetic (1936) he interprets proofs by strategies in a game : instead of just saying that A is true, the strategy gives an interactive way to check its truth against any opponent. It is irrelevant to notice that in reductionist terms this A proof B (strictly) contains the flat ....
G. Gentzen. Die Widerspruchsfreiheit der Stufenlogik. Mathematische Zeitschrift, 41.3:357--366, 1936.
Cumulative Higher-Order Logic as a Foundation for Set Theory - Degen, Johannsen (Correct)
.... can be formalized in PRA. Then it is obvious that the proof of the Theorem 6 can also be formalized. Hence PRA proves that K e and K e are equiconsistent. Now the consistency of K e can be trivially proved in PRA, by considering the standard model (V ; 2) along the lines of Gentzen [8]. 2.4 The In nitary Systems K 1 In order to get essentially stronger systems, we introduce a very natural in nitary inference rule, similar to the rule in arithmetic. It is motivated by the intention that the set of objects of a limit type should be the union of the sets of objects of ....
Gerhard Gentzen. Die Widerspruchsfreiheit der Stufenlogik. Mathematische Zeitschrift, 41:357-366, 1936.
The Independence of Peano's Fourth Axiom from Martin-Löf's.. - Jan M. Smith (1988) (8 citations) (Correct)
....March 1987 1 Introduction In Hilbert Ackermann [2] there is given a simple proof of the consistency of first order predicate logic by reducing it to propositional logic. Intuitively, the proof is based on interpreting predicate logic in a domain with only one element. Tarski [7] and Gentzen [1] have extended this method to simple type theory by starting with an individual domain consisting of a single element and then interpreting a higher type by the set of truth valued functions on the previous type. I will use the method of Hilbert and Ackermann on Martin Lof s type theory without ....
G. Gentzen. Die Widerspruchsfreiheit der Stufenlogik. Mathematische Zeitschrift 41, No. 3, 1936, pp.357-366.
Cumulative Higher-Order Logic as a Foundation for Set Theory - Degen, Johannsen (Correct)
....can be formalized in PRA. Then it is obvious that the proof of the Theorem 6 can also be formalized. Hence PRA proves that K e ff and K e are equiconsistent. Now the consistency of K e can be trivially proved in PRA, by considering the standard model (V ; 2) along the lines of Gentzen [8]. The Infinitary Systems K 1 ff In order to get essentially stronger systems, we introduce a very natural infinitary inference rule, similar to the rule in arithmetic. It is motivated by the intention that the set of objects of a limit type fl should be the union of the sets of objects of ....
Gerhard Gentzen. Die Widerspruchsfreiheit der Stufenlogik. Mathematische Zeitschrift, 41:357--366, 1936.
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