**Course:**Math 570 (Intro to Logic and Computability)/Phil 006 (Formal Logic II)/Lgic 310 (Logic I)

**Instructor:**Henry Towsner

**E-mail:**htowsner@math.upenn.edu

**Office:**4N51

**Office Hours:**Wednesday 1-2, Thursday 10:30-12:30, or by appointment

**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.

### Homework

Homework will be assigned roughly weekly, usually on Friday, and will be due the following Friday.### Exams

There will be two exams, an in-class midterm on October 25th and a take-home final due at 2pm on Monday, December 16.### Grades

Grades will be based on: 40 Homework, 30% Midterm, 30% Take Home Final.### Corrections

If 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.

### 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
- G\"odel coding
- The First Incompleteness Theorem
- Peano Arithmetic
- The Second Incompletness Theorem