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Lecturer(s)
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Course content
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1. Axioms of Set Theory (Zermelo-Fraenkel axiomatic system, language of set theory, formulas, classes). 2. Ordinal Numbers (well-ordering, ordinal numbers, transfinite induction and recursion, ordinal arithmetic). 3. Cardinal Numbers (cardinality, alephs, cofinality). 4. The Axiom of Choice (the Axiom of Choice, equivalent forms of the Axiom of Choice, using the Axiom of Choice in mathematics). 5. Cardinal Arithmetic (basic operations, infinite sums and products, the continuum function, cardinal exponentiation). 6. The Axiom of Regularity (the cumulative hierarchy of sets, well-founded relations). 7. Selected Topics in Set Theory (large cardinals, combinatorial set theory).
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training)
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Learning outcomes
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The main goal is to become familiar with the basic notions and results in axiomatic set theory.
Students define the basic concepts of set theory, investigate their properties and relationships between them.
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Prerequisites
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Knowledge of basic mathematical logic and naive set theory is assumed.
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Assessment methods and criteria
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Mark, Oral exam
Credit: active knowledge demonstration. Exam: understanding of the subject, proofs of the main theorems.
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Recommended literature
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Balcar B., Štepánek P. (2005). Teorie množin. Academia Praha.
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Bukovský L. (2005). Množiny a všeličo okolo nich. UPJŠ v Košiciach.
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Jech T. (2003). Set Theory. Springer-Verlag Berlin Heidelberg.
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