MA007 Mathematical Logic

Faculty of Informatics
Autumn 2009
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)
doc. RNDr. Tomáš Brázdil, Ph.D. (seminar tutor)
RNDr. Vojtěch Forejt, Ph.D., LL.B. (Hons) (seminar tutor)
RNDr. Jan Krčál, Ph.D. (seminar tutor)
Mgr. Marek Trtík, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Antonín Kučera, Ph.D.
Timetable
Tue 12:00–13:50 D2
  • Timetable of Seminar Groups:
MA007/01: each odd Thursday 16:00–17:50 B204, T. Brázdil
MA007/02: each even Thursday 16:00–17:50 B204, J. Krčál
MA007/03: each odd Thursday 18:00–19:50 B204, T. Brázdil
MA007/04: each even Thursday 18:00–19:50 B204, J. Krčál
Prerequisites
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 / plans the course is directly associated with
there are 32 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. 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
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.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2009, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2009/MA007