CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Mathematical Logic

Code Completion Credits Range Language
01MAL Z,ZK 4 2+1 Czech
Garant předmětu:
Petr Cintula
Lecturer:
Petr Cintula
Tutor:
Petr Cintula
Supervisor:
Department of Mathematics
Synopsis:

Logic is in the same time an object studied by mathematics and the language used to formalize and study mathematics. The goal of the course is to introduce basic notion of results of classical mathematical logic.

1.Propositions, evaluation, tautologies, axioms, theorems, soundness, completeness, and decidability of Hilbert and Gentzen style propositional calculi.

2.Language of predicate calculus, terms, formulas, relational structures, satisfiability, truth, tautologies, axioms, theorems, soundness, model constructions.

3.Gödel completeness theorem, Skolem and Herbrand theorems.

4.The first and the second Gödel theorems on incompleteness of Peano arithmetics and undecidability of predicate calculus.

Requirements:
Syllabus of lectures:

Logic is in the same time an object studied by mathematics and the language used to formalize and study mathematics. The goal of the course is to introduce basic notion of results of classical mathematical logic.

1.Propositions, evaluation, tautologies, axioms, theorems, soundness, completeness, and decidability of Hilbert and Gentzen style propositional calculi.

2.Language of predicate calculus, terms, formulas, relational structures, satisfiability, truth, tautologies, axioms, theorems, soundness, model constructions.

3.Gödel completeness theorem, Skolem and Herbrand theorems.

4.The first and the second Gödel theorems on incompleteness of Peano arithmetics and undecidability of predicate calculus.

Syllabus of tutorials:
Study Objective:

Knowledge:

Basic notions and results of classical propositional and predicate mathematical logic.

Skills:

Orientation in basics of mathematical logic and ability to use it in other disciplines.

Study materials:

Compulsory literature:

[1] V. Švejdar: Logika - neúplnost, složitost a nutnost. Academia, Praha 2002.

Optional literature:

[2] Nicholas J. J. Smith. Logic: The Laws of Truth. Princeton University Press, 2012.

Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-08-14
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