M7532 Logic foundations of mathematics

Faculty of Science
Autumn 2010 - only for the accreditation
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
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Some aspects of 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 G\"odel-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
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
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 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 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.