 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Algebra and Logic

The course is not on the list Without time-table
Code Completion Credits Range Language
BI-ALO Z,ZK 4 2P+1C Czech
Lecturer:
Tutor:
Supervisor:
Department of Applied Mathematics
Synopsis:

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

Requirements:

Basic course in predicate 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

T. Jech: Set Theory

K. Kunen: Foundations of Mathematics

Note:
Further information:
https://courses.fit.cvut.cz/BI-ALO/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2020-09-19
For updated information see http://bilakniha.cvut.cz/en/predmet5069606.html