Algebra and Logic

Garant předmětu:

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:

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/

No time-table has been prepared for this course

The course is a part of the following study plans:

• Bachelor program Informatics, unspecified branch, in Czech, 2015-2020 (elective course)
• Bachelor branch Security and Information Technology, in Czech, 2015-2020 (elective course)
• Bachelor branch Computer Science, in Czech, 2015-2020 (elective course)
• Bachelor branch Computer Engineering, in Czech, 2015-2020 (elective course)
• Bachelor branch Information Systems and Management, in Czech, 2015-2020 (elective course)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in Czech, 2015-2020 (elective course)
• Bachelor branch Web and Software Engineering, spec. Web Engineering, in Czech, 2015-2020 (elective course)
• Bachelor branch Web and Software Engineering, spec. Computer Graphics, in Czech, 2015-2020 (elective course)
• Bachelor branch Knowledge Engineering, in Czech, 2018-2020 (elective course)
• Bachelor specialization Information Security, in Czech, 2021 (elective course)
• Bachelor specialization Management Informatics, in Czech, 2021 (elective course)
• Bachelor specialization Computer Graphics, in Czech, 2021 (elective course)
• Bachelor specialization Computer Engineering, in Czech, 2021 (elective course)
• Bachelor program, unspecified specialization, in Czech, 2021 (elective course)
• Bachelor specialization Web Engineering, in Czech, 2021 (elective course)
• Bachelor specialization Artificial Intelligence, in Czech, 2021 (elective course)
• Bachelor specialization Computer Science, in Czech, 2021 (elective course)
• Bachelor specialization Software Engineering, in Czech, 2021 (elective course)
• Bachelor specialization Computer Systems and Virtualization, in Czech, 2021 (elective course)
• Bachelor specialization Computer Networks and Internet, in Czech, 2021 (elective course)
• Study plan for Ukrainian refugees (elective course)