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)
doc. RNDr. Tomáš Brázdil, Ph.D. (seminar tutor)
RNDr. Vojtěch Forejt, Ph.D., LL.B. (Hons) (seminar tutor)
- Guaranteed by
- prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science - Faculty of Informatics
Contact Person: prof. RNDr. Antonín Kučera, Ph.D.
- Thu 14:00–15:50 D2
- Timetable of Seminar Groups:
MA007/02: each even Thursday 8:00–9:50 B003, T. Brázdil
MA007/03: each odd Friday 13:00–14:50 B011, V. Forejt
MA007/04: each even Friday 13:00–14:50 B011, V. Forejt
- MB005 Foundations of mathematics || MB101 Mathematics I
It is necessary to go in advance through the subject MB005 Foundations of mathematics or through the subject MB101 Mathematics I. It is recommended to go either in advance or simultaneously also through the subject 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 contents of this course consists of propositional and predicate logic. The topics covered comprise axioms of propositional and predicate logic, the notions of truth, validity and provability, theories of predicate logic and their models, Gödel completeness theorem and its consequences, including some pieces of information on complete theories.
- Propositional logic: propositional formulas, truth, provability, completeness theorem
- Predicate logic: predicate formulas
- Semantics of predicate logic: realizations, truth, validity
- Axioms of predicate logic: provability, correctness, deduction theorem
- Completeness theorem: theories, models, Gödel completeness theorem
- Compactness theorem, Löwenheim-Skolem theorem
- Complete theories: elementary equivalence, Los-Vaught 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
- Assessment methods (in Czech)
- Předmět je ukončen písemnou zkouškou.
- Language of instruction
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.