LecturerVasco BrattkaDepartment of Mathematics & Applied Mathematics University of Cape Town 
Course DescriptionLogic is the general theory of reasoning. The roots of this discipline go back to ancient times but since the late 19th century the field has seen a vast development. Due to the paradoxes which have been discovered after mathematics had been build on the language of set theory, a careful reinvestigation of the logical basis of mathematics became necessary. It was the idea of Hilbert's program to develop mathematics from sound and complete axioms in a systematic way. This program, in its original form, came to an end after Gödel proved his famous Incompleteness Theorem which roughly speaking shows that no such general axiomatic development is possible (even for arithmetic there is no axiom system which is both, sound and complete). Hence, it became clear that provability and truth are two different aspects of mathematical statements. In this course we will try to capture the elementary development of mathematical logic.In particular, we will cover the following topics:

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© 20052009 Vasco Brattka