M4155 Set Theory

Faculty of Science
Spring 2009
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jiří Rosický, DrSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M4155/01: Wed 13:00–13:50 M1,01017, M. Kunc
Prerequisites
! M4150 Set Theory && ( M1120 Fundamentals of Mathematics || FI:MB005 Foundations of mathematics || M1125 Fundamentals of Mathematics )
sets, mappings, partially ordered sets
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course introduces basic set theory. The goal is to learn a set theoretical way of thinking and its use in concrete situations. Among others, this makes students able to understand the concept of infinity.
Syllabus
  • 1. Set theory: origin of set theory, set theory as a fundament of mathematics, concept of infinity, the construction of natural and real numbers 2. Cardinal numbers: cardinal numbers, ordering of cardinal numbers, Cantor-Bernstein theorem, operations with cardinal numbers 3. Well-ordered sets: well-ordered sets, transfinite induction, operations with well-ordered sets 4. Ordinal numbers: ordinal numbers, ordering of ordinal numbers, ordinal arithmetic, countable ordinal numbers 5. Axiom of choice: axiom of choice, well-ordering principle, maximality principle, applications of the axiom of choice to cardinal arithmetics 6. Elements of axiomatic set theory.
Literature
  • J. Rosický, Teorie množin II., http://www.math.muni.cz/~rosicky/
  • KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL. Logika, algebry a grafy. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1989, 434 s. info
  • BALCAR, Bohuslav and Petr ŠTĚPÁNEK. Teorie množin. 1. vyd. Praha: Academia, 1986, 412 s. info
  • FUCHS, Eduard. Teorie množin. Vyd. 1. Brno: Rektorát UJEP, 1974, 176 s. info
Assessment methods
Lectures: presence recommended, homeworks given, not controled Exams: oral
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2009/M4155