SubjectsSubjects(version: 861)
Course, academic year 2019/2020
Mathematical Logic - NMAG331
Title: Matematická logika
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
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: English
Teaching methods: full-time
Additional information:
Guarantor: prof. RNDr. Jan Krajíček, DrSc.
Class: M Bc. MMIB
M Bc. MMIB > Doporučené volitelné
M Bc. OM
M Bc. OM > Zaměření MA
M Bc. OM > Zaměření MSTR
M Bc. OM > Povinně volitelné
Classification: Informatics > Discrete Mathematics
Mathematics > Discrete Mathematics
Incompatibility : NLTM006
Interchangeability : NLTM006
XP//In complex pre-requisite: NMAG349
Annotation -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (05.09.2013)
An advanced course in mathematical logic. It breifly recalls basic concepts and costructions. The main topic is the incompleteness and the undecidability, and Godel's theorems in particular. A recommended course for specializations Mathematical Analysis and Mathematical Structures within General Mathematics.
Aim of the course - Czech
Last update: prof. RNDr. Jan Krajíček, DrSc. (10.09.2019)

Cílem je nahlédnout do problematiky logických základů matematiky a vyložit zejména algoritmickou nerozhodnutelnost

Halting problému a Godelovu větu o neúplnosti.

Course completion requirements -
Last update: prof. RNDr. Jan Krajíček, DrSc. (14.07.2019)

Oral exam, see

Literature -
Last update: doc. RNDr. David Stanovský, Ph.D. (25.09.2018)

Lou van den Dries: Lecture notes on mathematical logic,

J.R.Shoenfield: Mathematical logic; Addison-Wesley Publishing Company, London . Don Mills, Ontario, 1967.

Requirements to the exam -
Last update: prof. RNDr. Jan Krajíček, DrSc. (14.07.2019)


Syllabus -
Last update: prof. RNDr. Jan Krajíček, DrSc. (14.07.2019)

A review of basics of first-order logic, including elements of model theory. Peano arithmetic PA, formalization of syntax in PA. Godel's theorems. Turing machines, the universal machine, the undecidability of the halting problem.

See also

Entry requirements -
Last update: doc. RNDr. David Stanovský, Ph.D. (25.09.2018)

This is an informal continuation of NMAG162 Introduction of mathematical logic. The students are expected to understand basic syntactic and semantic properties of propositional and predicate logics.

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