## MA007 Mathematical Logic

Faculty of Informatics
Autumn 2002
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Jiří Kaďourek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments - Faculty of Science
Contact Person: doc. RNDr. Jiří Kaďourek, CSc.
Timetable
Fri 8:00–9:50 D2
Prerequisites
! M007 Mathematical Logic && ( M005 Foundations of mathematics || MB005 Foundations of mathematics || MB101 Foundations of mathematics I || SOUHLAS )
It is necessary to go in advance through the subject MB005 Foundations of mathematics or through the subject MB101 Mathematics I. It is recommended to go either in advance or simultaneously also through the subject MB008 Algebra I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
Fields of study the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
The contents of this course consists of propositional and predicate logic. The topics covered comprise axioms of propositional and predicate logic, the notions of truth, validity and provability, theories of predicate logic and their models, Gödel completeness theorem and its consequences, including some pieces of information on complete theories.
Syllabus
• Propositional logic: propositional formulas, truth, provability, completeness theorem
• Predicate logic: predicate formulas
• Semantics of predicate logic: realizations, truth, validity
• Axioms of predicate logic: provability, correctness, deduction theorem
• Completeness theorem: theories, models, Gödel completeness theorem
• Compactness theorem, Löwenheim-Skolem theorem
• Complete theories: elementary equivalence, Los-Vaught theorem
Literature
• MENDELSON, Elliott. Vvedenije v matematičeskuju logiku [Mendelson, 1976] : Introduction to mathematical logic (Orig.). Moskva: Nauka [Moskva], 1976. 319 s. info
• ŠTĚPÁNEK, Petr. Matematická logika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1982. 281 s. info
• KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL. Logika, algebry a grafy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989. 434 s. info
Assessment methods (in Czech)
Předmět je ukončen písemnou zkouškou.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019.
• Enrolment Statistics (Autumn 2002, recent)