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FI:MA007 Mathematical Logic - Course Information

## MA007 Mathematical Logic

**Faculty of Informatics**

Autumn 2006

**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. Petr Hliněný, Ph.D. (lecturer)

prof. RNDr. Antonín Kučera, Ph.D. (lecturer)

doc. RNDr. Tomáš Brázdil, Ph.D. (seminar tutor) **Guaranteed by**- prof. RNDr. Mojmír Křetínský, CSc.

Department of Computer Science - Faculty of Informatics

Contact Person: prof. RNDr. Petr Hliněný, Ph.D. **Timetable**- Wed 14:00–15:50 D3
- Timetable of Seminar Groups:

*T. Brázdil*

MA007/02: each odd Thursday 8:00–9:50 B007,*T. Brázdil*

MA007/03: each even Thursday 10:00–11:50 B007,*T. Brázdil*

MA007/04: each odd Thursday 10:00–11:50 B007,*T. Brázdil* **Prerequisites**- !
**M007**Mathematical Logic && (**M005**Foundations of mathematics ||**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 12 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.
**Syllabus**- 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

**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.
**Assessment methods**(in Czech)- Předmět je ukončen písemnou zkouškou.
**Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

The course is taught annually.

- Enrolment Statistics (Autumn 2006, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2006/MA007