Subjects

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MSTR Elective 1 - NMAG498

Title:	Výběrová přednáška z MSTR 1
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://diliberti.github.io/Teaching/Teaching%20Charles/SMC/2021/SMC21.html
Note:	you can enroll for the course repeatedly

Guarantor:	doc. RNDr. Jan Šťovíček, Ph.D.
Class:	M Mgr. MSTR M Mgr. MSTR > Volitelné
Classification:	Mathematics > Algebra

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (30.05.2023)

Non-repeated universal elective course.

Course completion requirements - Czech

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)

Předmět je zakončen ústní zkouškou.

Literature -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (03.06.2021)

T. Wedhorn, Manifolds, Sheaves, and Cohomology (https://www.springer.com/gp/book/9783658106324)

Requirements to the exam -

Last update: doc. RNDr. Jan Šťovíček, Ph.D. (11.10.2017)

The course is completed with an oral exam. The requirements for the exam correspond to what is presented in lectures.

Syllabus -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (30.05.2023)

ZS 2024/25: Obecné teorie logických systémů

1. Basic syntactical notions. Introduction of important examples (classical logic, intuitionistic logic, Lukasiewicz logic, Gödel-Dummett logic, BCI, and BCK). Completeness w.r.t. the general matrix semantics. Weakly implicative logics and completeness w.r.t. reduced models. Finitary logics and completeness w.r.t. relatively subdirectly irreducible matrices. Characterizations of completeness properties w.r.t. arbitrary classes of models.

2. Generalized disjunctions and proof by cases properties. Semilinear logics and their characterizations. Examples in the family of substructural logics.

3. Leibniz operator on arbitrary logics. Leibniz hierarchy: protoalgebraic, equivalential and (weakly) algebraizable logics. Regularity and finiteness conditions. Alternative characterizations of the classes in the hierarchy. Bridge theorems connecting algebraic and metalogical properties (e.g. deduction theorems, Craig interpolation, Beth definability).