Lectures on Mathematical Logic

The publication presents mathematical logic in the context of its philosophical background and from a historical perspective as an essential and indispensable part of human culture. The first two chapters are devoted to this aim. The following two chapters focus on propositional calculus and first-order logic, that is, on “mandatory” topics appearing in most logic textbooks. In the book, however, they are treated largely in parallel, so that both their similarities and their differences stand out clearly. Going beyond this “mandatory” framework, the book includes a detailed proof of Gödel’s Completeness Theorem for first-order logic. The next four chapters address topics that have not yet been published in book form in the Slovak-language ambience. The fifth chapter introduces the reader to Gödel’s Incompleteness Theorems, including their mathematical as well as philosophical aspects and consequences. The final three chapters (Substructures and Homomorphisms, Preservation Theorems, Ultraproducts and Axiomatic Classes) offer a brief introduction to model theory. This modern mathematical discipline is also referred to as the “metamathematics of algebra”. In addition to providing a unifying perspective on a substantial part of algebra, it also brings a range of methods and results that enrich not only algebra but also mathematical analysis and other areas of mathematics.

Autor: prof. RNDr. Pavol Zlatoš, PhD. 
Recenzenti: prof. RNDr. Miroslav Haviar, PhD., prof. RNDr. Ladislav Kvasz, DSc. 

ISBN: 978-80-223-6123-1