A Unification
Raymond Smullyan · 2008
This chapter generalizes many of the most important results in first-order logic. It presents “Theorem AM”—a very abstract result about arbitrary sets, rather than just sets of formulas; this theorem makes no reference at all to logical connectives or quantifiers but has applications to first-order logic (as well as to other possible logics). The chapter also presents a very elaborate puzzle about variable liars, whose solution is virtually tantamount to proving the Completeness Theorem for Tableaux. It generalizes the solutions to the puzzle and the results T1-T6 of first-order logic. The Model Existence Theorem is particularly useful in the field known as Infinitary Logic. For first-order logic, the Unification Theorem is preferred.