# PH210: Logic II Metatheory

##### Term 1 2015-2016, 15 CATS

Module tutor: Walter Dean (W dot H dot Dean at warwick dot ac dot uk)

Logistics:

• Lecture 1: Monday 11:00-13:00 P2.51
• Lecture 2: Wednesday 11:00-12:00 M2.04
• Seminar: Wednesday 10:00-11:00 F1.10
• Office hour: Monday 13:00-14:00 S2.70

### Problem sets

Description:

This module will develop the metatheory of propositional and first-order logic. The primary goal is to show that a proof system similar to that of Logic I is sound (i.e. proves only logically true sentences) and complete (proves all logically true sentences). In order to better understand how we prove things about (as opposed to within) a proof system, we will first study elementary set theory and inductive definitions. We will then consider Tarski's definitions of satisfaction and truth in a model and proceed to develop the Henkin completeness proof for first-order logic. Other topics covered along the way will include Russell's Paradox, countable versus uncountable sets, the compactness theorem, the expressive limitations of first-order logic, as well as and (time permitting) an overview of intuitionistic, modal, and second-order logic.

Textbooks:

Our primary text will be

- Logic and Structure, 4th edition by Dirk van Dalen, Springer Verlag, 2004

in which we will cover most of chapters 1-3. The same material is also covered at a more elementary level in chapters 15-19 of

- Language, Proof and Logic, Jon Barwise and John Etchemendy, CSLI Publications, 2002.

Students lacking a background in elementary discrete maths (e.g. basic set theory and mathematical induction) are encouraged to obtain

- How to prove It: A Structured Approach, Daniel J. Velleman, Cambridge University Press, 2006.

Students considering taking further logic modules will also benefit from looking at

- The Open Logic Book (which is part of the Open Logic Project)