Oxford University Press Fragments of First-Order Logic - Oxford Logic Guides

Fragments of First-Order Logic explores the fundamental question of algorithmic satisfiability in mathematical logic, examining whether formulas can be determined true within specific structures. While Church and Turing proved in 1936 that general satisfiability is undecidable, and Trakhtenbrot demonstrated the same for finite satisfiability in 1950, this Oxford Logic Guides volume investigates restricted subsets of first-order logic where these problems become algorithmically solvable. The book addresses the theoretical foundations of logic by distinguishing between satisfiability (truth in some structure) and finite satisfiability (truth in finite structures), providing essential insights for mathematicians and logicians studying decidability, computational complexity, and the boundaries of algorithmic methods in formal systems.