Class times: Mondays and Wednesdays, 10.10-11.25am

Class location: Caldwell Hall, Room 213

- Professor: Gillian Russell
- Email: gillian_russell@unc.edu
- Office hours: Mondays 11.25am-12.25pm and Fridays 1.30-2.30pm
- Office Location: 2nd Floor of Caldwell Hall (upstairs, then turn right twice.)

This is a course in the model theory, proof theory and metatheory of first-order classical logic, aimed at students who have taken at least one course in formal logic in the past. In the first part of the class we will study sentential logic and practice some skills that we want to apply later, especially proof by induction and the production of informal proofs. Then in the second part we will work our way through the First-Order Logic sections of the Open Logic Project (OLP) textbook. Among the topics we will cover are sequent calculus proofs, completeness, compactness, and the Löwenheim-Skolem theorem.

N.B. Until Wednesday 11th October there is no pre-assigned reading. Starting 2nd October there will be a section from the “First-Order Logic” chapter of the Open Logic Project to be read before class.

Introduction to the course.

Soundness and Validity

Syntax for the sentential language

Interpretations

Logical Properties

No class – Labour Day

Informal Proofs

Normal forms

Expressive adequacy

Proof by induction

No class.

Expressive adequacy revisited

~~Post Completeness~~ Syntax revisited

First-order syntax (I)

Reading: pages 52-56 of *The Open Logic Project (OLP)*

Review Session for the Midterm

In Class Midterm Examination

First-order syntax (II)

Pages 56-63 of (OLP)

First-order structures

Pages 64-74.

First-order Logical Properties

pages 74-78.

Theories and Models

Pages 79-84

More First-order Theories

Pages 85-89

Sequent Calculus (I)

Pages 90-103

No class.

Sequent Calculus (II)

Pages 103-110

Soundness

Pages 110-117.

Completeness (I)

Pages 142-149

Completeness (II)

Pages 149-151

Adding Identity

Pages 151-154

No class – Thanksgiving

Compactness and the Löwenheim-Skolem Theorem

Pages 154-159

“Catch Up” class (in case any of the above topics take more time than planned)

Final exam.

- 50% of your grade will come from the problem sets. (I’ll drop your worst grade and average the rest.)
- 25% of your grade will come from the in-class midterm examination.
- 25% of your grade will come from the final examination.

I will give out (either in class or by email) solutions to the problem sets approximately one week after the assignments

are due. Any work turned in after the solutions have been given out will receive a zero.

Since the two exams are an important part of your grade, you should make sure that

you will be on campus to take them before you decide to take this course.

Our textbook has a helpful manual containing some recommendations and hints for students attempting the problems. I recommend that you take a look.

Assessment |
Due Date |

Problem set 1 | Friday 1st September |

Problem set 2 | Friday 15th September |

Problem set 3 | Friday 6th October |

Midterm Examination | Wednesday 9th October |

Problem set 4 | Friday 27th October |

Problem set 5 | Friday 17th November |

Problem set 6 | Friday 1st December |

Final Examination | Friday 15th December, 8am |

Problem sets should be turned in by placing them in my mailbox on the 1st floor of Caldwell

Hall by 3pm on the day they are due.

It is important that you understand the rules for working with other students on this course. You may work with other students in order to work out solutions to the problems in the take-home problem sets; in fact, I encourage you to do this. However, you must write up your homework answers on your own. You may not write your homework from notes which another student has made, nor may you make notes on another student’s written solutions. You may not lend or copy digital or paper homework solutions at any stage of completion.

One way of working within these rules is to work through ideas for solving the problems with others using an erasable white or blackboard (or paper which you dispose of) and then wipe it clean before you each write up your homework alone.

Sometimes it may be unclear whether a certain action would be permissible according to the rules above, but it is your responsibility to ensure that your actions are always clearly permissible.

All students must be familiar with and abide by the Honor Code, which covers issues such as plagiarism, falsification, unauthorized assistance or collaboration, cheating, and other grievous acts of academic dishonesty. Violations of the Honor Code will not be taken lightly.

Located in the Student Academic Services Building, the CSSAC offers support to all students through units such as the Learning Center and the Writing Center.

Any student in this course who has a disability that may prevent them from fully demonstrating their abilities should contact Disability Services as soon as possible to discuss accommodations.

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