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Course detail
Mathematical Logic
Course unit code:  FSISML  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Master's (2nd cycle)  
Year of study:  1  
Semester:  summer  
Number of ECTS credits:  5  



























Type of course unit:
Lecture:  26 hours, optionally 

Teacher / Lecturer:  prof. RNDr. Josef Šlapal, CSc. 
Syllabus:  1. Introduction to mathematical logic 2. Propositions and their truth, logic operations 3. Language, formulas and semantics of propositional calculus 4. Principle of duality, applications of propositional logic 5. Formal theory of the propositional logic 6. Provability in propositional logic, completeness theorem 7. Language of the (firstorder) predicate logic, terms and formulas 8. Semantic of predicate logics 9. Axiomatic theory of the firstorder predicate logic 10.Provability in predicate logic 11. Theorems on compactness and completeness, prenex normal forms 12.Firstorder theories and their models 13.Undecidabilitry of firstorder theories, Gödel's incompleteness theorems 
seminars:  26 hours, compulsory 
Teacher / Lecturer:  Mgr. Jan Pavlík, Ph.D. 
Syllabus:  Relational systems and universal algebras 1. Sets, cardinal numbers and cardinal arithmetic 2. Sentences, propositional connectives, truth tables,tautologies and contradictions 3. Independence of propositional connectives, axioms of propositional logic 4. Deduction theorem and proving formulas of propositional logic 5. Terms and formulas of predicate logics 6. Interpretation, satisfiability and truth 7. Axioms and rules of inference of predicate logic 8. Deduction theorem and proving formulas of predicate logic 9. Transforming formulas into prenex normal forms 10.Firstorder theories and some of their models 11.Monadic logics SkS and WSkS 12.Intuitionistic, modal and temporal logics, Presburger arithmetics 