This is a companion to a paper by the authors entitled “Gödel’s natural deduction,” which presented and made comments about the natural deduction system in Gödel’s unpublished notes for the elementary logic course he gave at the University of Notre Dame in 1939. In that earlier paper, which was itself a companion to a paper that examined the links between some philosophical views ascribed to Gödel and general proof theory, one can find a brief summary of Gödel’s notes for the (...) Notre Dame course. In order to put the earlier paper in proper perspective, a more complete summary of these interesting notes, with comments concerning them, is given here. (shrink)

This article presents three extracts from the introductory course in mathematical logic that Gödel gave at the University of Notre Dame in 1939. The lectures include a few digressions, which give insight into Gödel's views on logic prior to his philosophical papers of the 1940s. The first extract is Gödel's first lecture. It gives the flavour of Gödel's leisurely style in this course. It also includes a curious definition of logic and a discussion of implication in logic and natural language. (...) The second extract is a discussion on undecidability and on Leibniz. The third extract concerns the paradoxes and Russell's theory of types. (shrink)

As initially envisioned, Gödel's Collected Works were to include transcriptions of material from his mathematical workbooks. In the end that material, as well as some other manuscript items from Gödel's Nachlass, had to be left out. This note describes some of the unpublished items in the Nachlass that are likely to attract the notice of scholars and surveys the extent of shorthand transcription efforts undertaken hitherto. Some examples of sources outside Gödel's Nachlass that may be of interest to Gödel scholars (...) are also indicated. (shrink)

The paper is a brief survey of some sequent calculi which do not follow strictly the shape of sequent calculus introduced by Gentzen. We propose the following rough classification of all SC: Systems which are based on some deviations from the ordinary notion of a sequent are called generalised; remaining ones are called ordinary. Among the latter we distinguish three types according to the proportion between the number of primitive sequents and rules. In particular, in one of these types, called (...) Gentzen’s type, we have a subtype of standard SC due to Gentzen. Hence by nonstandard ones we mean all these ordinary SC where other kinds of rules are applied than those admitted in standard Gentzen’s sequent calculi. We describe briefly some of the most interesting or important nonstandard SC belonging to the three abovementioned types. (shrink)

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

The initial volume of a comprehensive edition of Gödel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936. The volume begins with an informative overview of Gödel's life and work and features facing English translations for all German originals, extensive explanatory and historical notes, and a complete biography. Volume 2 will contain the remainder of Gödel's published work, and subsequent volumes will include unpublished manuscripts, lectures, correspondence and extracts from (...) the notebooks. (shrink)