This book is a record of a seminar on mathematical logic Kurt Gdel and Hans Hahn held in Vienna in 1931-32. The seminar proceedings, given in English translation, are a unique witness of the state of research in logic and foundations of mathematics right after Gdel had published his celebrated incompleteness theorems. The seminars explain Gdel's results in logic in detail, in contrast to his publications of the time that often were quite laconic and extremely short. This book also contains Gdel's trial lecture on intuitionistic logic held in Vienna in 1933. The manuscript, recently found among the Gdel papers kept in Princeton, is preserved in Gdel's forgotten German shorthand and published here in an English translation.

The book also adds an important aspect to the intellectual history of Vienna, as both Gdel and Hahn were members of the Vienna Circle group of philosophers and scientists.