Gerhard Gentzen died on August 4, 1945, in a prison in Prague. His fellow prisoners were professors of the local German university, and there are accounts of his last days and how he was, rendered… Expand

The aim of this paper is to investigate the relationship of the two approaches within a very general framework, to discuss the viability of erecting logic on such austere foundations, and to find out whether choosing one of the ways the authors are inevitably led to a specific logical system is chosen.Expand

In this thesis I provide a survey over different approaches to second-order logic and its interpretation, and introduce a novel approach. Of special interest are the questions whether (a particular… Expand

The proof-irrelevant model defined in Smith (1988) is extended to the whole of Martin-Löf's logical framework, and it is useful to obtain an elementary proof of consistency and to prove the independence of Peano's fourth axiom.Expand

It is shown that several axiomatic first-order set theories can be interpreted in K∞ α, for suitable α, and a semantic completeness theorem for K ∞ α is proved by the method of reduction trees.Expand

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness… Expand

« Oui c’est imbecile ce que je dis ! Seulement je ne sais pas comment concilier tout ca. Il est sur que je ne me sens libre que parce que j’ai fait mes classes et que je ne sors de la fugue que parce… Expand