Mathematical logic. On numbers, sets, structures, and symmetry
type: Item
instance of: scholarly article
title: Mathematical logic. On numbers, sets, structures, and symmetry
zbMATH Open document ID: 1462.03002
DOI: 10.1007/978-3-319-97298-5
author: Roman Kossak
published in: Springer Graduate Texts in Philosophy
publication date: 2018-09-28T00:00:00Z
review text: Remembering how impenetrable textbooks on mathematical logic were when he was a freshman, the author has written an introductory textbook on mathematical logic, whose main strength is the emphasis on motivating every step with detailed explanations. While there are theorems in the book, such as compactness, completeness, and much more, there are no proofs, as the aim is to convey how mathematical logic looks at structures, how formalism captures essential features of structures. The structures studied are finite graphs, the natural numbers, the integers, the rationals, real numbers, complex numbers, and sets. After a first part devoted to introducing the above structures, a second part studies more advanced topics, such as elementary extensions, minimal, order-minimal structures, strongly minimal structures, the Seidenberg-Tarski theorem, the MRDP theorem, a comparison of the arithmetic of natural numbers and that of complex numbers, a mention of the fact that there is a countable model of set theory. Each chapter ends with exercises. Some proofs are presented in an appendix. The author has clearly succeeded in writing a textbook making the reading of those impenetrable texts possible for a beginner.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 03-01
Mathematics Subject Classification ID: 03Bxx
Mathematics Subject Classification ID: 03E30
zbMATH DE Number: 6945597
zbMATH Keywords: structures
zbMATH Keywords: order-minimal structures
zbMATH Keywords: minimal structures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-97298-5
OpenAlex ID: W4248046334
description: scientific article; zbMATH DE number 6945597