ADVANCED LOGIC: METATHEORY

 

This course will demonstrate some of the fundamental metatheoretical results about classical logic.  These include the soundness, completeness, and undecidability of first-order logic.  Along the way, we cover some basics of computability theory.  This prepares us to give an overview of Gödel's well-know incompleteness results.  We finish by discussing some considerations from second-order logic. 
 

Course Text:

 

Sets, Logic, and Computation, Remixed by Richard Zach (Open Logic Project)

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Assessment:

 

Exercise sets, one mid term, and one final examination.

 

Course Schedule:

 

Week 1: Sets, relations and functions

 

Week 2: First-order logic: syntax

 

Week 3: First-order logic: semantics

 

Week 4: Theories and their models

 

Week 5: Derivation systems

 

Week 6: Sequent calculus

 

Week 7: Natural deduction

 

Week 8: Completeness

 

Week 9: Turing machine computations

 

Week 10: Undecidability

 

Week 11: Incompleteness

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Week 12: Second-order logic

 

 

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