Math 6010 Spring 2015

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Course Information:

This will a seminar/class on topics in mathematical logic. the intention is to focus on topics related to the incompleteness phenomenon, but other topics will be covered along the way or in addition. We will start by proving the Gödel incompleteness theorem, in its various forms, developing the necessary theotry of recursive functions and models of arithmetic along the way. After this, we will consider examples of incompleteness such as Hilbet's 10th problem, the word problem in group theory, etc. This will involve a mixture of logic, number theory, and algebra. We will develop all the necessary background as we go. As time permits, we will then study incompleteness in arithmetic such as Goodstein sequences, strong Ramsey properties, etc.
We will not use a single book as a text for the class, but I will be giving out notes, which will also. be posted here.

Here are some notes on recursive functions (work in progress), arithmetic, and the Gödel incompleteness theorem to get started. recursive, arithmetic, Gödel.