Set theory, independence proofs and the continuum hypothesis
Informacje ogólne
Kod przedmiotu: | 1000-2M23STI |
Kod Erasmus / ISCED: |
11.3
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Nazwa przedmiotu: | Set theory, independence proofs and the continuum hypothesis |
Jednostka: | Wydział Matematyki, Informatyki i Mechaniki |
Grupy: |
Przedmioty monograficzne dla matematyki 2 stopnia Przedmioty obieralne dla informatyki |
Punkty ECTS i inne: |
3.00
|
Język prowadzenia: | angielski |
Rodzaj przedmiotu: | monograficzne |
Wymagania (lista przedmiotów): | Podstawy matematyki 1000-211bPM |
Skrócony opis: |
(tylko po angielsku) The course will provide an introduction to set theory and independence proofs, with the goal of ultimately proving that the famous Continuum Hypothesis is independent of Zermelo Fraenkel axioms of set theory. The course will be made as accessible as possible (and will review basic notions from logic and model theory), but at least some previous knowledge of first-order logic will be useful. Note: Course is given in English. |
Pełny opis: |
(tylko po angielsku) Relationship of logic, set theory and mathematics: review of basic notions of logic (proof system, completeness theorem, Lowenheim-Skolem theorem, etc), discussion of mathematics vs metamathematics (2-3 lectures) Zermelo Fraenkel set theory: axioms, well-ordered sets, ordinals, transfinite induction and recursion (3-4 lectures) Independence proofs via inner models: independence of the axiom of regularity, constructible universe, absoluteness, consistency of the axiom of choice and continuum hypothesis (4-5 lectures) Forcing: models of set theory (standard models, minimal model), forcing as a technique, independence of the axiom of choice and the continuum hypothesis (4-5 lectures) |
Literatura: |
(tylko po angielsku) Book “Set Theory and the Continuum Hypothesis” by Paul Cohen Book “Set Theory: An Introduction to Independence Proofs” by Kenneth Kunen Lecture notes provided by the lecturer |
Efekty uczenia się: |
(tylko po angielsku) The student will have understanding of basic notions of set theory, will be able to prove independence results and have a basic working knowledge of the forcing method |
Metody i kryteria oceniania: |
(tylko po angielsku) Oral exam The course can provide credit for doctoral students as a "methodological course". In that case, there is an additional requirement for passing the course: The student should correctly solve an assignment given by the lecturer, or study and present a result assigned by the lecturer. |
Zajęcia w cyklu "Semestr letni 2023/24" (w trakcie)
Okres: | 2024-02-19 - 2024-06-16 |
Przejdź do planu
PN WT ŚR CZ WYK
PT |
Typ zajęć: |
Wykład, 30 godzin
|
|
Koordynatorzy: | Jakub Gajarský | |
Prowadzący grup: | Jakub Gajarský | |
Lista studentów: | (nie masz dostępu) | |
Zaliczenie: | Egzamin |
Właścicielem praw autorskich jest Uniwersytet Warszawski.