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Course, academic year 2022/2023
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Fundamentals of Mathematical Logic - NLTM006
Title: Základy matematické logiky
Guaranteed by: Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Josef Mlček, CSc.
Classification: Informatics > Theoretical Computer Science
Incompatibility : NAIL062
Interchangeability : NMAG331
Is incompatible with: NMAG331
Is pre-requisite for: NAIL049
Is interchangeable with: NMAG331
Annotation -
Last update: T_KTI (13.05.2003)
A basic course of first-order logic with an introduction to the model theory. A problem of undecidability and formal consistency is treated.
Aim of the course -
Last update: RNDr. Jan Hric (07.06.2019)

To learn fundamentals of propositional and predicate logic

Course completion requirements -
Last update: RNDr. Jan Hric (07.06.2019)

Oral exam

Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)
  • J.R.Shoenfield: Mathematical logic; Addison-Wesley Publishing Company, London . Don Mills, Ontario, 1967
  • E.Mendelson: Introduction to Mathematical Logic; D.Van Nostrand Company, INC., Princeton, New Jersey, Toronto, New York, London 1964 (fourth edition 1977 Chapman & Hall ISBN 412 80830 7)
  • H.D.Ebinghaus, J.Flum, W.Thomas: Mathematical Logic, Springer-Verlag 1984 ISBN 0-387-90895-1
  • K.Čuda: Základy matematické logiky; učební text
  • P. Štěpánek: Predikátová logika
  • P. Štěpánek: Meze formální metody

Syllabus -
Last update: T_KTI (13.05.2003)

Propositions and first-order logic: language, deduction, theory, algebras of formulas. Models of theories, an existence of models, completeness and compactness theorem. Corollaries. Interpretations of theories. Basic model theory: homomorphism, isomorphism and elementary embedding, categoricity, algebras of definable sets. Undecidability and incompleteness: recursive formalization of the syntax, predicates "to be a theorem" and "to be an inconsistent theory", Gödel's theorems.

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