Paolo Mancosu | Searcharxiv

arXiv2023

Some Unpublished Letters by Gödel and von Neumann in the Fraenkel Archive

Several letters by Kurt Gödel and Johann (János) von Neumann from the (so far uncatalogued) archive of Abraham (Adolf) Fraenkel at the National Library of Israel are published and discussed. These include two fragments by Gödel of special interest, since they concern the relationship between Gödel's incompleteness theorem and work by Herbrand, Presburger, and Zermelo, as well as a long letter from von Neumann from 1923 explaining his own approach to the axiomatization of set theory.

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arXiv2015

Heinrich Behmann's 1921 lecture on the decision problem and the algebra of logic

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved-independently of Löwenheim and Skolem's earlier work-the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included.

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