Course for international guest/part time students
- Faculty
- Faculty of Humanities
- Organization
- BTK Institute of Philosophy
- Code
- BMI-FILD-301
- Title
- Foundations of logic
- Usual semester
- Autumn
- ECTS
- 4
- Language
- Learning outcomes
- For the latest version of the syllabus, please visit the Philosophy course catalogue: http://lps.elte.hu/courselist/ The course provides an introduction to first-order logic. Content of the course: • Syntacs of first-order languages • Sets, relations, functions • Semantics of first-order languages • Central logical notions in first-order logic • Deductive systems • Soundness and completeness • First-order theories • Peano arithmetic • Infinite sets and set theory • Löwenheim-Skolem theorem • Limits of first-order logic and the idea of second-order logic Required reading: P. D. Magnus and T. Button, forallx:Cambridge, 2017. J. Barwise and J. Etchemendy, Language, Proof and Logic. CSLI Publications, 2011. Suggested further reading: H. Halvorson, How Logic Works: A User's Guide. Princeton, NJ: Princeton University Press, 2020. I. Chiswell and W. Hodges, Mathematical Logic. Oxford University Press, 2007.
- Course content
- For the latest version of the syllabus, please visit the Philosophy course catalogue: http://lps.elte.hu/courselist/ Content of the course: The lecture and exercise class together provide an introduction to mathematical logic. During this course we cover all the fundamental concepts and techniques that are inevitable for any further studies during the Logic and Theory of Science progam. Although there are no formal prerequisites, certain level of maturity of abstract thinking is expected. For students who are more interested in the deeper understanding of the material the Set theory course offered by the department is recommended. In the lecture we focus on the two most important formal logical frameworks. • Class 1-4. Basics of Propositional logic: syntax and semantics, proof theory. • Class 5-13. Basics of First-order logic: syntax and semantics, basic model and proof theory. Completeness and Compacteness theorem, Löweheim-Skolem theorems. Limits of first-order logic. The lecture is accompanied by an exercise class in which we practice and see applications of the concepts and techniques we covered in the lectures.
- Assessment method
- Grading criteria: (oral) exam
- Bibliography
- References [1] David Marker. An invitation to mathematical logic. Springer. 2024. [2] László Csirmaz, Zalán Gyenis Mathematical logic. Exercises and solutions. Springer. 2022.