M4150 Set theory

Faculty of Science
Spring 2000
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Mgr. Martin Ander, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Prerequisites (in Czech)
M1120 Fundamentals of mathematics
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
Syllabus
  • Complete lattices: distributive lattices, directed sets, complete posets, compact elements, algebraic lattices
  • Cardinal numbers: cardinal numbers, ordering of cardinal numbers, Cantor-Bernstein theorem, operations with cardinal numbers
  • Well-ordered sets: well-ordered sets, transfinite induction, operations with well-ordered sets
  • Ordinal numbers: ordinal numbers, ordering of ordinal numbers, ordinal arithmetic, countable ordinal numbers
  • Axiom of choice: axiom of choice, well-ordering principle, maximality principle
  • Cardinal arithmetic: cardinal arithmetic
  • Applications of set theory: bases of vector spaces, linear orderings, trees, measures and measurable sets, filters and ultrafilters
Literature
  • 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
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2001, Spring 2002, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019.
  • Enrolment Statistics (Spring 2000, recent)
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