Classical mathematical logic. (Q2753072)

This is a textbook on classical zero and first-order logic. The first two chapters contain the standard basic material (formulas and their semantics, Hilbert style axiomatization, completeness) on propositional, resp., predicate calculi. The next one deals with various subjects related, in some way or other, with provability in first-order logic: introducing new symbols, conservative extensions, Hilbert-Ackermann theorem on open theories, Herbrand and Skolem theorems. There is also a chapter containing elements of model theory. Two chapters are of more specific character. One of them treats formal arithmetic (including arithmetization of syntax and various incompleteness theorems) and Turing machines, while the small final chapter is devoted to decidability and iterpretability of theories, and to interpolation theorems. Each chapter is accompanied by exercises, which provide a wealth of supplementary material on subjects not discussed in the main text. The reader will find a number of themes (for instance, the so-called Goodstein theorem) discussed in Czech for the first time.