An Introduction to Mathematical Logic
Résumé
These are the lecture notes of a course on mathematical logic for master students in mathematics given in 2024-2025 at the university of Rennes. The document is entirely self-contained and does not suppose any prerequisite. Some parts of these lectures notes are sometimes largely based on or copied verbatim from publications of other authors. When this is the case, these parts are mentioned at the end of each chapter in the section “Suggested further reading”. In particular, all the figures that appear in the second part on non-standard analysis stem from the book of H. J. Keisler, "Elementary Calculus: an Approach Using Infinitesimals" (1986, Prindle and Weber & Schmidt), an online edition of this book is freely available on the website https://people.math.wisc.edu/~hkeisler/calc.html. Another important reference is the book of E. Mendelson, "Introduction to mathematical logic" (2010, CRC press, 5th edition). These lecture notes are complemented by the document "Seminar: introduction to set theory" written by Romain Azam and which is available on HAL at https://hal.science/hal-04777494.
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