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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
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
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

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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.