PřF:M6531 Set Theory I - Course Information

M6531 Set Theory I

Faculty of Science
Spring 2000

Extent and Intensity

2/0/0. 3 credit(s). Type of Completion: graded credit.

Teacher(s)

doc. RNDr. Eduard Fuchs, CSc. (lecturer)

Guaranteed by

Prerequisites (in Czech)

M3510 Algebra III && M4502 Mathematical Analysis III

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

Problems of infinity in mathematics. Origins of set theory and its impact on the 20th century mathematics. Formalization of mathematics: propositional calculus, first order logic calculus, axiomatic theories. Axioms for set theory: Zermelo-Fraenkel set theory and G\"odel-Bernays set theory, construction of natural and real numbers in set theory. Cardinal and ordinal numbers: ordering and arithmetics of cardinal numbers, arithmetics of ordered sets, ordinal types and their arithmetics, well-ordering sets, ordinal numbers, transfinite induction. Axiom of choise and equivalent theorems. Peano arithmetics.

Literature

FUCHS, Eduard. Teorie množin pro učitele. 1st ed. Brno: Masarykova univerzita, 1999. info
FUCHS, Eduard. Základy teorie množin. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 146 s. info
FUCHS, Eduard. Logika a teorie množin : (úvod do oboru). Vyd. 1. Brno: Rektorát UJEP, 1978, 175 s. info
FUCHS, Eduard. Teorie množin. Vyd. 1. Brno: Rektorát UJEP, 1974, 176 s. info
BLAŽEK, Jaroslav, Emil CALDA and Blanka KUSSOVÁ. Algebra a teoretická aritmetika. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1979, 244 s. info
TARSKI, Alfred. Úvod do logiky a metodologie deduktivních věd. Translated by Pavel Materna. Vyd. 1. Praha: Academia, 1966, 245 s. URL 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 Spring 2001, Spring 2002.