FI:MA007 Mathematical Logic - Course Information
MA007 Mathematical LogicFaculty of Informatics
- 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).
- prof. RNDr. Antonín Kučera, Ph.D. (lecturer)
RNDr. Jan Krčál, Ph.D. (seminar tutor)
RNDr. Petr Novotný, Ph.D. (seminar tutor)
Mgr. Bc. Tomáš Janík (assistant)
- Guaranteed by
- prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science - Faculty of Informatics
Contact Person: prof. RNDr. Antonín Kučera, Ph.D.
- Tue 10:00–11:50 D2
- Timetable of Seminar Groups:
MA007/02: each even Tuesday 14:00–15:50 B204, J. Krčál
MA007/03: each odd Wednesday 14:00–15:50 G125, P. Novotný
MA007/04: each odd Tuesday 14:00–15:50 B204, P. Novotný
- MB005 Foundations of mathematics || MB101 Mathematics I || 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 24 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
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.
- 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.
- 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
- Teaching methods
- Lectures and tutorials.
- Assessment methods
- Lectures: 2 hours/week. Tutorials: 1 hour/week.
- Language of instruction
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.