M7532 Logic foundations of mathematics

Faculty of Science
Autumn 2015
Extent and Intensity
2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: graded credit.
Teacher(s)
doc. RNDr. Eduard Fuchs, CSc. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 10:00–11:50 M2,01021
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 / plans the course is directly associated with
Course objectives
Some formal aspects of mathematics are studied. The main objectives of the couurses is the Godel theorem of incompleteness.
Syllabus
  • Origins of set theory and its impact on the 20th century mathematics.
  • Formalization of mathematics: propositional calculus, first order logic calculus, axiomatic theories.
  • Axioms for set theory: Zermelo-Fraenkel set theory and Gödel-Bernays set theory, construction of natural and real numbers in set theory.
  • Cardinal and ordinal numbers: ordering and arithmetics of cardinal numbers, arithmetics of ordered sets, ordinal types and their arithmetics, well-ordering sets, ordinal numbers, transfinite induction.
  • Axiom of choise and equivalent theorems.
  • Peano arithmetics.
Literature
  • FUCHS, Eduard. Teorie množin pro učitele. 1st ed. Brno: Masarykova univerzita, 1999. info
  • FUCHS, Eduard. Základy teorie množin. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 146 s. info
  • FUCHS, Eduard. Logika a teorie množin : (úvod do oboru). Vyd. 1. Brno: Rektorát UJEP, 1978, 175 s. info
  • FUCHS, Eduard. Teorie množin. Vyd. 1. Brno: Rektorát UJEP, 1974, 176 s. info
  • BLAŽEK, Jaroslav, Emil CALDA and Blanka KUSSOVÁ. Algebra a teoretická aritmetika. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1979, 244 s. info
  • TARSKI, Alfred. Úvod do logiky a metodologie deduktivních věd. Translated by Pavel Materna. Vyd. 1. Praha: Academia, 1966, 245 s. URL info
Teaching methods
Theoretical explanation with practical examples
Assessment methods
Written test (50 % success rate)
Language of instruction
Czech
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 1999, Spring 2008 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.
  • Enrolment Statistics (Autumn 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2015/M7532