česky | **in English**

Autumn 2016

**Extent and Intensity**- 2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
**Teacher(s)**- prof. RNDr. Antonín Kučera, Ph.D. (lecturer)

Mgr. David Klaška (seminar tutor)

Bc. Tomáš Lamser (seminar tutor) **Supervisor**- prof. RNDr. Mojmír Křetínský, CSc.

Department of Computer Science - Faculty of Informatics

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

Supplier department: Department of Computer Science - Faculty of Informatics **Timetable**- Mon 12:00–13:50 A217
- Timetable of Seminar Groups:

*T. Lamser*

MA007/02: each odd Wednesday 12:00–13:50 C525,*D. Klaška*

MA007/03: each even Thursday 14:00–15:50 C525,*D. Klaška*

MA007/04: each odd Thursday 14:00–15:50 C525,*T. Lamser* **Prerequisites**-
**MB005**Foundations of mathematics ||**MB101**Linear models ||**MB201**Linear models B ||**PřF:M1120**Discrete Mathematics ||**PřF:M1125**Fundamentals of Mathematics

Students should have passed the course`MB005`Foundations of mathematics or the course`MB101`Mathematics I. A recommended course is`MB008`Algebra I. **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 the course is directly associated with**- there are 25 fields of study the course is directly associated with, display
**Course objectives**- The course covers basic results about propositional and first
order logic, including Gödel's completeness and incompleteness
theorems.

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 [Mendelson, 1976] : Introduction to mathematical logic (Orig.)*. Moskva: Nauka [Moskva], 1976. 319 s. info - ŠTĚPÁNEK, Petr.
*Matematická logika*. 1. vyd. 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)**- Study Materials

The course is taught annually.

- Enrolment Statistics (Autumn 2016, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2016/MA007

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