IA046 Computability

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: z (credit).
Teacher(s)
prof. RNDr. Luboš Brim, CSc. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Luboš Brim, CSc.
Timetable
Tue 12:00–13:50 B411
Prerequisites
! I046 Computability II
Prerequisities: IB107 Computability and Complexity,MA006 Set Theory
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na hlubší studium výsledků teorie vyčíslitelnosti s důrazem na osvojení si používaných důkazových metod a technik.
Syllabus
  • Recursion theorem, generalized Rice theorem, Rogers isomorphism theorem. Applications.
  • Application to logic. Arithmetical sets and functions, Goedel-Rosser incompleteness theorem. Goedel's second incompleteness theorem.
  • Relativized computability. Programs with oracles.
  • Kleene hierarchy, Turing reducibility, tt-reducibility, arithmetical hierarchy.
  • Post's problem.
  • Analytical hierarchy, applications to logic.
  • Computability on real numbers, complete partial orders, domains.
Literature
  • Theory of Recursive Functions and Effective Computability. Edited by Hartley Rogers. Cambridge: Massachusetts Institute of Technology, 1987, 482 s. ISBN 0262680521. info
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.fi.muni.cz/usr/brim/I046
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.
  • Enrolment Statistics (Autumn 2002, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2002/IA046