Goedel's Incompleteness Theorem

Credits 8 credit points
Instructors Barendregt, H.P. (Radboud Universiteit Nijmegen), Oosten, J. van (Universiteit Utrecht)
E-mail henk@cs.ru.nlj.vanoosten@uu.nl
Aim To understand one of the fundamental issues of
metamathematics
Organization The axiomatic method was described by Aristotle:
mathematics consists of objects and properties.
Objects can be obtained from primitive ones using definitions.
Properties can be established from axioms using proofs.
The Gödel first incompleteness theorem states that contradiction free axiomatic systems as least as strong as arithmetic are incomplete. This means that there are statements A that can neither be proved nor be refuted.
The second incompleteness theorem states that, although consistency can be formulated in systems as least as strong as arithmetic, this statement is among the undecided ones. In spite of this the axiomatic method is all we have and it is quite powerful.
Examination Written exam: May 26, 14:00-17:00h. Science Park C0.110. Some extra tests will be given that can increase but cannot decrease the final mark.
Literature  Lecture notes can be downloaded here.
Prerequisites Some mathematical experience.
Remarks More information you can find here.
  Last changed: 18-06-2014 12:59