M5150 Mathematical Logic

Faculty of Science
Autumn 2003
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Kaďourek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Jiří Kaďourek, CSc.
Timetable of Seminar Groups
M5150/01: No timetable has been entered into IS. J. Kaďourek
Prerequisites
M1120 Fundamentals of Mathematics || M1125 Fundamentals of Mathematics
It is necessary to go in advance through the subject M1120 Discrete mathematics. In addition, it is also recommended to go in advance through the subject M2150 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
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. 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
Assessment methods (in Czech)
Předmět je ukončen písemnou zkouškou.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2004.
  • Enrolment Statistics (Autumn 2003, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2003/M5150