PH210: Logic II Metatheory
Term 1 20152016, 15 CATS
Module tutor: Walter Dean (W dot H dot Dean at warwick dot ac dot uk) Logistics:



Current announcements

Problem sets 
This module will develop the metatheory of propositional and firstorder 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 firstorder logic. Other topics covered along the way will include Russell's Paradox, countable versus uncountable sets, the compactness theorem, the expressive limitations of firstorder logic, as well as and (time permitting) an overview of intuitionistic, modal, and secondorder 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 13. The same material is also covered at a more elementary level in chapters 1519 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)