M5150 Mathematical Logic

Faculty of Science
Autumn 2001
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Kaďourek, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Jiří Kaďourek, CSc.
Prerequisites
M1120 Fundamentals of mathematics
It is necessary to go in advance through the subject M1120 Discrete mathematics. In addition, it is recommended either to go through in advance or to enrol simultaneously the subject M3110 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
  • KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL. Logika, algebry a grafy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989, 434 s. info
  • ŠTĚPÁNEK, Petr. Matematická logika. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 281 s. info
Assessment methods (in Czech)
Předmět je ukončen písemnou zkouškou.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2002, Autumn 2003, Autumn 2004.
  • Enrolment Statistics (Autumn 2001, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2001/M5150