Richard Zach is Professor at the University of Calgary.
"The Decision Problem and Logical Metatheory"
The emergence of first-order logic and its metatheory is commonly seen as a switch from a purely axiomatic development of the logical systems in the Hilbert school to a metalogical view that incorporates model-theoretic methods. One origin of these model-theoretic methods undoubtedly can be found in the work of Skolem and later Gödel and Tarski, to whom they are usually credited. Nevertheless, work on the decision problem during the 1920s in the Hilbert school itself independently gave rise to model-theoretic thinking, occasioned by the needs for proving decidability. The episode shows how mathematical practice can force fundamental changes in methodology.
