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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023

Algebra and Logic

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Code Completion Credits Range Language
BI-ALO Z,ZK 4 2P+1C Czech
Lecturer:
Jan Starý (guarantor)
Tutor:
Jan Starý (guarantor)
Supervisor:
Department of Applied Mathematics
Synopsis:

The course extends and deepens the study of topics touched upon in the basic course in logic.

Requirements:

A basic course in mathematical logic.

Syllabus of lectures:

1. Predicate logic revisited: provability, correctness.

2. The completeness of predicate logic (Gödel's theorem)

3. Henkin completion. Compactness.

4. Prenex form. Skolem functions.

5. Resolution: Skolemization, Unification.

6. Resolution in predicate logic

7. Axioms of set theory.

8. Well orders, ordinal numbers.

9. Ordinals as types of well orders.

10. Axioms of choice, maximality principles.

11. Cardinalities, cardinal numbers.

12. Dedekind completion, real numbers.

Syllabus of tutorials:

1. Provability

2. Consequences of compactness in algebra

3. Skolemization, unification, rezolution.

4. Natural numbers, integers, rationals.

5. AC iff every vector space has a basis.

6. Real numbers.

Study Objective:
Study materials:

J. Barwise: Handbook of Mathematical Logic

K. Kunen: Foundations of Mathematics

T. Jech: Set Theory

Note:
Further information:
https://courses.fit.cvut.cz/BI-ALO/
Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-12-02
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