Instructor: Henry Towsner
Office Hours: Wednesday 1-2, Thursday 10:30-12:30, or by appointment
Office Phone: (215) 898-8474
TextbookThe 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.
HomeworkHomework will be assigned roughly weekly, usually on Friday, and will be due the following Friday.
ExamsThere will be two exams, an in-class midterm on October 25th and a take-home final due at 2pm on Monday, December 16.
GradesGrades will be based on: 40 Homework, 30% Midterm, 30% Take Home Final.
CorrectionsIf you believe there is a mistake on any grading, you have two weeks from when the item is handed back to bring it to my attention.
SyllabusMath 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
- G\"odel coding
- The First Incompleteness Theorem
- Peano Arithmetic
- The Second Incompletness Theorem