Mathematical logic. On numbers, sets, structures, and symmetry (Q1785529)

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.