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The decision problem: Solvable classes of quantificational formulas

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TLDR
In this article, the authors provide a unified treatment of the positive results of the decision problem for quantification theory, and delimit the boundary between solvable and unsolvable classes of formulas.
Abstract
Solvable Classes of Quantificational Formulas Burton Dreben and Warren D. Goldfarb, Harvard Univ. Skolem and Herbrand addressed the decision problem by associating with each quantificational formula a set, usually infinite, of quantifier-free formulas. In this book, the authors build on that insight to illuminate the mathematical structures underlying solvability, and provide for the first time a unified treatment of the positive results of the decision problem for quantification theory. The results of this book, together with those of Lewis's Unsolvable Classes of Quantificational Formulas, delimit the boundary between solvable and unsolvable.

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