# FI:MA007 Mathematical Logic - Course Information

## MA007 Mathematical Logic

**Faculty of Informatics**

Autumn 2024

**Extent and Intensity**- 2/1/1. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).

Taught in person. **Teacher(s)**- prof. RNDr. Antonín Kučera, Ph.D. (lecturer)

Dr. rer. nat. Achim Blumensath (seminar tutor)

Bc. Vít Jelínek (seminar tutor)

RNDr. David Klaška (seminar tutor) **Guaranteed by**- prof. RNDr. Antonín Kučera, Ph.D.

Department of Computer Science – Faculty of Informatics

Contact Person: prof. RNDr. Antonín Kučera, Ph.D.

Supplier department: Department of Computer Science – Faculty of Informatics **Prerequisites**-
**IB000**Math. Foundations of CS ||**PřF:M1120**Discrete Mathematics ||**PřF:M1125**Fundamentals of Mathematics

Students should have passed the course`IB000`Mathematical Foundations of Computer Science or a course covering the foundations of mathematics at the Faculty of Science. **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Informatics (programme FI, B-INF) (2)

**Course objectives**- The course covers basic results about propositional and first order logic, including Gödel's completeness and incompleteness theorems.
**Learning outcomes**- At the end of this course, students should be able to:

understand the difference between formal notions and notions defined at a meta-level;

understand the difference between validity and provability;

understand the syntax and semantics of first-order logic;

understand and appreciate the fundamental ideas in the proofs of Gödel's completeness and incompleteness theorems. **Syllabus**- Propositional calculus: propositional formulas, truth, provability, completeness.
- First-order logic: syntax, semantics.
- A deductive system for first-order logic. Provability, correctness.
- Completeness theorem: theories, models, Gödel's completeness theorem
- Basic model theory, Löwenheim-Skolem theorem
- Gödel's incompleteness theorem.

**Literature**- MENDELSON, Elliott.
*Vvedenije v matematičeskuju logiku*. Edited by Sergej Ivanovič Adjan, Translated by F. A. Kabakov. Izd. 2-oje, ispr. Moskva: Nauka. Glavnaja redakcija fiziko-matematičeskoj literatury, 1976, 320 s. info - ŠTĚPÁNEK, Petr.
*Matematická logika*. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 281 s. info - KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL.
*Logika, algebry a grafy*. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989, 434 s. info

- MENDELSON, Elliott.
**Teaching methods**- Lectures and tutorials.
**Assessment methods**- Lectures: 2 hours/week. Tutorials: 1 hour/week.

Written exam. **Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- The course is taught annually.

The course is taught: every week.

- Enrolment Statistics (Autumn 2024, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2024/MA007