# Phil 450

## Intermediate Symbolic Logic

This course will be taught from Boolos, Burgess, and Jeffrey, *Computability and Logic*

My office hours are Thursday, 2-4 pm.

There will be weekly proofs to write up (listed below), and each student will present proofs in class approximately once a week. There will be no final exam.

The readings and topics we will cover are (in order) the following:

## Chapter 1 - enumerability

## Chapter 2 - uncountability

## Chapter 9 - syntax of first-order logic

## Chapter 10 - semantics of first-order logic

## Chapter 6 - primitive recursive functions

## Chapter 7 - recursive functions and relations

## Chapter 15 - computability and logic

## Chapter 16 - representation of recursive functions in logic

## Chapter 17 - the first incompleteness theorem

## If you want a second source on any of this material, ask me for other notes.

Written homework assignments:

All exercises are from the Boolos, Burgess, and Jeffrey book unless otherwise mentioned.

Tuesday, September 3: Exercise 1.4

Tuesday, September 17: Exercise 2.2

Tuesday, September 24: Exercise 2.11

Tuesday, October 1: Show that every term has a formation sequence in which only sub-terms of that term appear.

Tuesday, October 8: Exercises 10.2, 10.3

Tuesday, October 15: Exercises 1 and 2 from section 1.4 of the handout on deductions

Tuesday, October 22: The Negation Theorem, section 3.2.4 of the handout on deductions

Tuesday, October 29: Exercises 6.7, 6.8

Tuesday, November 6: Exercises 7.5, 7.6, 7.7

Tuesday, November 12 (no assignment)

Tuesday, November 19: Exercises 15.6, 15.7

Tuesday, November 26: Exercise 17.8

Solutions to exercises that have already been turned in.