Goedel's Incompleteness Theorem
Tarig Abdel Gadir
Friday 13th February, 2009 16:00-17:00 Mathematics Building, room 516
In the 1920s Hilbert set up a programme (later conveniently named Hilbert's programme) to formalise all existing mathematical theories to a finite set of consistent axioms. In the 1930s Goedel showed that any finite set of axioms defining the natural numbers is not 'complete' and so proved that Hilbert's programme is unachievable. I will state Goedel's Incompleteness theorem and outline a proof. I will assume notions from basic logic such as logical operators, truth tables and logical equivalence.