# Course - Logic MT24

> Source: https://ollybritton.com/notes/uni/part-b/mt24/logic/ · Updated: 2025-06-26 · Tags: uni, course

> This course is a rigorous introduction to the basics of mathematical logic. The course is divided into two halves, the first covering propositional logic and the second covering first-order logic, and is mainly concerned with proving results about logic rather than its applications. Both halves follow the same structure; first discussing the syntax, then the semantics, then a proof system, followed by the completeness and compactness of that proof system.

- [Course Webpage](https://courses.maths.ox.ac.uk/course/view.php?id=5533)
- [Lecture Notes](https://people.maths.ox.ac.uk/bays/teaching/b1logic/B1.1.pdf)
- Related:
	- [Course - Set Theory HT25](https://ollybritton.com/notes/uni/part-b/ht25/set-theory/)
	- [Course - Logic and Proof MT24](https://ollybritton.com/notes/uni/part-b/mt24/logic-and-proof/)
- [Dr. Marin Bays](https://people.maths.ox.ac.uk/bays/) wrote the lecture notes for this course, and the notes here are adapted from those notes.
- Other courses this term: [Courses MT24](https://ollybritton.com/notes/uni/part-b/mt24/)

### Notes
- [Notes - Logic MT24, Basic definitions for propositional logic](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/basic-definitions-for-propositional-logic/)
- [Notes - Logic MT24, Proofs in propositional logic](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/proofs-in-propositional-logic/)
- [Notes - Logic MT24, Example proofs in propositional logic](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/example-proofs-in-propositional-logic/)
- [Notes - Logic MT24, First-order logic](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/first-order-logic/)
- [Notes - Logic MT24, Proofs in first-order logic](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/proofs-in-first-order-logic/)
- [Notes - Logic MT24, Example proofs in first-order logic](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/example-proofs-in-first-order-logic/)
- [Notes - Logic MT24, Gödel's completeness theorem](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/godels-completeness-theorem/)
- [Notes - Logic MT24, Compactness theorems](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/compactness-theorems/)
- [Notes - Logic MT24, Löwenheim-Skolem theorem](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/lowenheim-skolem-theorem/)
- [Notes - Logic MT24, Isomorphisms of structures](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/isomorphisms-of-structures/)
- [Notes - Logic MT24, Unbounded dense linear orders](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/unbounded-dense-linear-orders/)
- [Notes - Logic MT24, Axiomatisations](https://ollybritton.com/notes/uni/part-b/mt24/logic/notes/axiomatisations/)

### Problem Sheets
- [Sheet 1](https://courses.maths.ox.ac.uk/pluginfile.php/105519/mod_assign/introattachment/0/B1.1-sheet1.pdf)
- [Sheet 2](https://courses.maths.ox.ac.uk/pluginfile.php/105520/mod_assign/introattachment/0/B1.1-sheet2.pdf)
- [Sheet 3](https://courses.maths.ox.ac.uk/pluginfile.php/105521/mod_assign/introattachment/0/B1.1-sheet3.pdf)
- [Sheet 4](https://courses.maths.ox.ac.uk/pluginfile.php/105522/mod_assign/introattachment/0/B1.1-sheet4.pdf)

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