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

TL;DR

Heinrich Behmann's 1921 lecture presents an independent solution to the decision problem for monadic second-order logic, combining algebraic and axiomatic methods, and discusses the importance of decision procedures in logic.

Contribution

The paper introduces a novel solution to the decision problem for monadic second-order logic, independent of L"owenheim and Skolem, using algebraic and axiomatic approaches.

Findings

Solution to the decision problem for monadic second-order logic

Integration of algebra of logic with axiomatic methods

Discussion on the significance of decision procedures

Abstract

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in G\"ottingen in 1921 with a thesis on the decision problem. In his thesis, he solved-independently of L\"owenheim 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 G\"ottingen. 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.