| Course title | Logic and Set Theory |
|---|---|
| Course code | KAG/LTM |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | 1 |
| Semester | Summer |
| Number of ECTS credits | 4 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Propositional logic, semantics of the propositional logic, conjunctive and disjunctive normal form. 2. Hilbert propositional calculus, the notion of a formal proof, deduction theorem, soundness and completeness theorem for propositional logic. 3. First-order (predicate) logic, languages, terms and predicate formulas, structures, validity and satisfiability (Tarski's truth definition). 4. Hilbert predicate calculus, deduction theorem, soundness and completeness theorem for predicate logic. 5. Infinity in mathematics, paradoxes of infinity and of set theory, axiom-like principles for set constructions. 6. The algebra of sets, relations, basic properties of binary relations. 7. Field of real numbers and its basic properties, natural numbers as the smallest inductive subset of the real numbers, mappings and their elementary properties. 8. Cardinality of sets, Cantor - Bernstein Theorem and its consequences. 9. Finite sets (Dedekind and Tarski definitions), countable sets, basic examples and assertions concerning countable sets, uncountable sets. 10. Arithmetical operations on the cardinalities, Cantor Theorem (cardinality of the power set). 11. Well-ordering, axiom of choice, transfinite induction. 12. Metamathematics of set theory, ZFC axiomatics of set theory.
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| Learning activities and teaching methods |
| Monologic Lecture(Interpretation, Training) |
| Learning outcomes |
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The main aim is to become familiar with the basic notions and results in mathematical logic and naive set theory.
1. Knowledge: Students define the basic concepts of logic and set theory, investigate their properties and relationships between them. |
| Prerequisites |
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Knowledge of basic mathematical concepts is assumed.
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| Assessment methods and criteria |
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Oral exam
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| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Mathematics (2020) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Summer |