Introduction to Logic
This is a basic logic course covering topics from recursion theory, model theory and set theory. The following is the list of topics that we will cover.
|1. compactness theorem and incompleteness theorem (0-1 laws and etc).|
|2. Back and fourth arguments (uniqueness of countable dense orders)|
|3. quantifier elimination and applications to algebra (Hilberts Nullstelenzats and etc)|
|4. Godel's constructible universe (Consistency of Axiom of Choice and Continuum Hypothesis relative to ZF)|
|5. Cohen's forcing (Consistency of negation of CH relative to ZFC)|
Students interested in doing research in logic who have not yet passed their qualifying exam must take this course. Students interested in other areas of mathematics will profit from this course as well, as basic methods developed by logicians have found applications in many areas of mathematics, and this course will be an introduction to some of these methods.
A Concise Introduction to Mathematical Logic, Rautenberg
General Mathematical Maturity
Sections Taught This Semester:
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