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Mathematical Logic - NMAG331

Title:	Matematická logika
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://users.math.cas.cz/~jerabek/teaching/mathlog.html

Guarantor:	Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D.
Class:	M Mgr. MSTR > Povinně volitelné
Classification:	Informatics > Discrete Mathematics Mathematics > Discrete Mathematics
Incompatibility :	NLTM006
Interchangeability :	NLTM006
Is interchangeable with:	NLTM006
In complex pre-requisite:	NMAG349

Opinion survey results Examination dates WS schedule Noticeboard

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: Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D. (02.10.2023)

Cílem je nahlédnout do problematiky logických základů matematiky a vyložit zejména algoritmickou nerozhodnutelnost Halting problému a Gödelovu větu o neúplnosti.

Course completion requirements -

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

Oral exam, see http://www.karlin.mff.cuni.cz/~krajicek/zk-mll.html

Literature -

Last update: Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D. (02.10.2023)

Lou van den Dries: Lecture notes on mathematical logic, https://www.karlin.mff.cuni.cz/~krajicek/vddries.pdf

Michael Sipser: Introduction to the theory of computation, Thomson, 2006.

René Cori and Daniel Lascar: Mathematical logic: A course with exercises (Part I and Part II), Oxford University Press, 2000.

Joseph R. Shoenfield: Mathematical logic; Addison-Wesley Publishing Company, London, 1967.

Requirements to the exam -

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

Viz http://www.karlin.mff.cuni.cz/~krajicek/zk-mll.html

Syllabus -

Last update: Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D. (02.10.2023)

A review of basics of first-order logic, including elements of model theory.

Turing machines, the universal machine, the undecidability of the halting problem.

Peano arithmetic PA, Gödel’s theorems, formalization of syntax in PA.

See also https://users.math.cas.cz/~jerabek/teaching/mathlog.html and https://www.karlin.mff.cuni.cz/~krajicek/mll.html

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.