PřF:M4150 Set Theory - Course Information

M4150 Set Theory

Faculty of Science
Spring 2019

Extent and Intensity

2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Teacher(s)

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

Guaranteed by

Timetable

Mon 18. 2. to Fri 17. 5. Mon 12:00–13:50 M2,01021

Prerequisites (in Czech)

M7532 Foundations 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

Course objectives

First course of set theory. Cardinal and ordinal numbers, transfinite induction.

Syllabus

Problems of infinity in mathematics. Origins of set theory and its impact on the 20th century mathematics. 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 choice and equivalent theorems.

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
TARSKI, Alfred. Úvod do logiky a metodologie deduktivních věd. Translated by Pavel Materna. Vyd. 1. Praha: Academia, 1966, 245 s. URL info

Teaching methods

Theoretical explanation with practical examples

Assessment methods

One written test (50 % success rate)and oral exam.

Language of instruction

Czech

Follow-Up Courses

Further Comments

The course is taught annually.