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Course, academic year 2022/2023
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Advanced mathematical logic - NAIL111
Title: Pokročilá matematická logika
Guaranteed by: Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022 to 2022
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Josef Mlček, CSc.
Annotation -
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 -
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 -
Last update: RNDr. Jan Hric (07.06.2019)

Oral exam

Literature -
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 -
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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