|
Lecturer(s)
|
-
Botur Michal, doc. Mgr. Ph.D.
-
Kühr Jan, prof. RNDr. Ph.D.
|
|
Course content
|
1. Mathematical logic. Elementary means of the propositional logic, laws of propositional logic. 2. Determination of truth values of propositional formulas. Basic theorems on tautologies. Duality principle, complete systems and bases of logical connectives. 3. Conjunctive and disjunctive normal forms. 4. The elements of predicate logic. 5. Set theory: Zermelo-Fraenkel's axiom system. Cartesian product and its properties, relation of equivalence, relation of order. 6. Functions and their properties, the Zermelo theorem on the order function. 7. Equivalent sets and their cardinal numbers, cardinal arithmetic and inequality. 8. The Cantor-Bernstein theorem, the Cantor theorem and its consequences. Tarski's and Dedekind's definition of infinite sets, the Dedekind theorem. 9. Countable and uncountable sets, their examples and properties. Uncountable sets, properties of transfinite cardinal numbers. Peano's model of arithmetic of the set No, mathematical induction. Similarity of sets, well-ordered sets, transfinite induction. 10. Ordinal numbers, arithmetic of ordinal nubmers, inequalities. 11. Relation between the cardinal and the ordinal numbers.
|
|
Learning activities and teaching methods
|
|
Monologic Lecture(Interpretation, Training)
|
|
Learning outcomes
|
To understand the elements of mathematical logic and set theory.
1. Knowledge Students define and describe basic elements of the logic and the set theory and recognise the relationships between them.
|
|
Prerequisites
|
unspecified
|
|
Assessment methods and criteria
|
Oral exam
Credit: presentation of active knowledge. Exam: understand the subject and prove the major theorems.
|
|
Recommended literature
|
-
Balcar B., Štěpánek P. (1986). Teorie množin. Academia Praha.
-
MAC NIELLE H. M. (1979). Basic Set Theory. Springer-Verlag Berlin.
-
Rachůnek J. (1986). Logika. UP Olomouc.
-
Šalát T., Smítal. J. (1986). Teória množín. Alfa Bratislava.
|