Intermediate Logic

9 units · Undergraduate

Intermittent: 9 units The course builds on the proof theory and model theory of first-order logic covered in 21-300 . These are applied in 21-400 to Peano Arithmetic and its standard model, the natural numbers. The main results are the incompleteness, undefinability and undecidability theorems of Godel, Tarski, Church and others. Leading up to these, it is explained how logic is formalized within arithmetic, how this leads to the phenomenon of self-reference, and what it means for the axioms of a theory to be computably enumerable. Related aspects of computability theory are included to the extent that time permits. (Three 50 minute lectures) Prerequisite: 21-300