Oxford University Press - Fragments of First-Order Logic

Explore the fundamental questions of mathematical logic with Fragments of First-Order Logic from the Oxford Logic Guides series. This text examines the core concepts of satisfiability and finite satisfiability within first-order logic. It addresses the historical breakthroughs made by Church, Turing, and Trakhtenbrot regarding the algorithmic solvability of these problems. While general satisfiability was proven to be undecidable, this book focuses on the significant area of study where these problems become algorithmically solvable: restricted subsets of logic. By analyzing these fragments, readers gain a deeper understanding of the boundaries between decidability and undecidability. This work is an essential resource for those studying mathematical foundations and the limits of computational logic.