PH210 Logic II: Metatheory 20112012
Term 1 20112012, 15 CATS
Module tutor: Walter Dean (w dot h dot dean at warwick dot ac dot uk) Logistics:
The first lecture will take place on Monday 3 October. Seminars will start in week 2 (i.e. they will meet for the first time on 10 October). 


Current announcements

Problem sets

Description:
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 and 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.
Maths students considering taking further logic courses might consider getting a copy of
 The Mathematics of Logic, Richard Kaye, Cambridge University Press, 2007.