OXFORD LOGIC GUIDES Series Editors A.J. MACINTYRE D.S. SCOTT Emeritus Editors D.M. Gabbay John Shepherdson OXFORD LOGIC GUIDES For a full list of titles please visit http://www.oup.co.uk/academic/science/maths/series/OLG/ 21. C. McLarty: Elementary categories, elementary toposes 22. R.M. Smullyan: Recursion theory for metamathematics 23. Peter Clote and Jan Kraj´ıcek: Arithmetic, proof theory, an