SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Logic and set theory - NMUM505
Title in English: Logika a teorie množin
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Martin Rmoutil, Ph.D.
Incompatibility : NMUM818, NUMP016
Interchangeability : NMUM818, NUMP016
Annotation -
Last update: RNDr. Jakub Staněk, Ph.D. (17.06.2019)
A basic course in mathematical logic and set theory for prospective teachers.
Requirements to the exam -
Last update: RNDr. Martin Rmoutil, Ph.D. (17.06.2019)

The course is finished by passing an oral exam. Students will be asked to formulate and explain definitions, theorems and proofs from the lecture; there will be enough time to prepare written notes before discussing the questions with the examinator. A precise list of requirements will be available on the website of the lecturer.

Syllabus -
Last update: RNDr. Martin Rmoutil, Ph.D. (17.06.2019)

Basic notions of propositional and predicate calculus.

A general account of axiomatic theory, including a short mention of consistency and completeness.

The purpose and influence of set theory in mathematics.

Axioms of ZFC.

Comparing sets by cardinality, Cantor-Bernstein theorem, Cantor's theorem.

Natural numbers in set theory. Finite and countable sets.

Integer, rational and real numbers.

Ordinal numbers, their order, and operations on them.

Axiom of Choice and its equivalents.

Cardinal numbers, order and operations.

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