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A comprehensive and impressive book! All the fundamental results of First-order Logic (Propositional Logic and Predicate Logic), its extension in Peano Arithmetic Axiomatized (PAax) and, finally, a modal analysis of the idea of provability in PAax are subject of a detailed analysis. The whole theoretical developments are both syntactical and semantic, exposed in a variety of theorems, proved in a variety of forms. The Chapter 3, Formal Number Theory, is focused on Gödel’s Theorems, an analysis of their original forms and of some notable subsequent generalizations, based on Kleene’s T-predicate, recursive enumerability, recursive inseparability and Post’s creative sets. The final chapter, Modal Logic of Provability, is devoted to the relation between PAax and the modal system Gödel-Löb (GL), and is focused on two fundamental results on this topic: the arithmetical soundness and completeness of GL (Solovay’s Theorem) and the Fixed Point Theorem (Dick de Jongh – G. Sambin).
The high quality of analyses, the elegance of proofs and the notable scientific level of contents make from Mathematical Logic a distinguished book in the Romanian culture.
The book is for undergraduate, graduate and PhD students and researchers. |