Subjects(version: 941)
Title: Pokročilá matematická logika Department of Theoretical Computer Science and Mathematical Logic (32-KTIML) Faculty of Mathematics and Physics from 2022 to 2022 winter 3 winter s.:2/0, Ex [HT] unlimited unlimited no taught Czech full-time full-time
Guarantor: doc. RNDr. Josef Mlček, CSc.
 Annotation - ---CzechEnglish
Last update: T_KTI (12.04.2016)
Mathematical logic formulates and develops the concept of deduction, truth and an algorithmic solvability. It delivers a concept of axiomatic theories and their corresponding semantic realizations called models and allows to analyze such theories with regard to consistency, completeness, decidability, descriptive complexity, to the character of axioms etc. Moreover, it provides methods for construction of models and solves the problems of axiomatisability of classes of models. It includes beside classical two-valued logic also multi-valued, higher-order, modal, temporal and others.
 Aim of the course - ---CzechEnglish
Last update: T_KTI (12.04.2016)

The aim is to provide deeper and more comprehensive knowledge of mathematical logic and acquire them through important and numerous examples.

 Course completion requirements - ---CzechEnglish
Last update: RNDr. Jan Hric (07.06.2019)

Oral exam

 Literature - ---CzechEnglish
Last update: T_KTI (12.04.2016)

W. Hodges, Model theory, Cambridge University Press, 1993

F. Kröger, S. Merz, Temporal logic and state systems, Springer, 2008

W. Rautenberg, A concise introduction to mathematical logic, Springer, 2009

 Syllabus - ---CzechEnglish
Last update: RNDr. Jan Hric (27.04.2018)
• Deeper properties of classical first-order logic: arithmetization, diagonalization, formalization of proovability, strong, essential and hereditary unsolvability. Application (in set theory, arithmetics and another theories).
• Abstract logic systems. Characterizations o classical logic - Lindström theorem.
• Non-classical logic systems: second-order logic, infinitary logic (with examples), temporal logic.

A knowledge of basics of classical first-order logic is assumed.

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