Papers are usually presented in .dvi, .ps and .pdf form. Click on the title for the .dvi file, on .ps for the PostScript file, and on .pdf for the Acrobat file.

Should users find that any of the files here are corrupt, please inform the author. At present --- March 2015 --- email addresses for him are

ardm@email.mathematik.uni-freiburg.de

ardm@dpmms.cam.ac.uk

Very recent additions are marked by

Mathematical logic has come a long way since the work of Frege, the discovery by Russell of a contradiction in Frege's system, and the responses of Zermelo, Russell and Whitehead to that discovery. It is noticeable that many of the subsequent proposals for a single foundation of mathematics emphasize one aspect of mathematics at the expense of another, and for my part, I hold that, for reasons going back to the ancient Greek division between arithmetic and geometry, mathematics requires a dual foundation, a balance, which has yet to be achieved, between the insights of set theory and of category theory.

** A)**
A great advance in set theory occurred in 1935-8 with Gödel's creation of the notion of constructibility, the main technical tool
underlying his relative consistency proofs for the Axiom of Choice (AC) and the
Generalised Continuum Hypothesis (GCH).
A second great advance occurred when I was an undergraduate in the early 1960's, namely Cohen's creation of forcing, the main technical tool
underlying his independence proofs for AC and GCH.
This advance attracted me to set theory; and the papers in

** B,C)**
The next two lists study further the two sides of the dual foundation mentioned above.
The papers in

** D)**
The papers in

** E)**
Mathematics draws research projects from Natural Science: so it is natural to ask whether ordinals occur in Nature, and I was thus led, in my papers in

** List F** contains a miscellany of papers, largely written for the pure pleasure of solving attractive problems.

**List G** contains discussions of various philosophies of mathematics and a campaign article.

**List H** contains lecture notes, survey articles and shorter expository pieces.