Instructor: Henry Towsner
E-mail: htowsner@math.upenn.edu
Office: 4N51
Office Phone: (215) 898-8474
Textbook
The textbook for this class is Leary and Kristiansen, A Friendly Introduction to Mathematical Logic, 2nd ed., 2015. This text is freely available online.It may be helpful to refer Enderton, A Mathematical Introduction to Logic, which is on reserve in the library, but this book is not required.
Syllabus
Math 570 is an introduction to first-order logic and formal mathematical proof. The topics covered are:- The Completeness Theorem:
- Syntax of first-order logic: languages, terms, and formulas
- Sematics of first-order logic: structures and models
- Formal deductions and axioms
- The Completeness Theorem for first-order logic
- Consequences of completeness: compactness and Löwenheim-Skolem
- The Incompleteness Theorem:
- Formula complexity
- Gödel coding
- The First Incompleteness Theorem
- Peano Arithmetic
- The Second Incompletness Theorem