Richard Kaye's other research papers

This page lists some additional research papers (including some web or electronic papers, work in progress, etc.) More substantial publications including books and other major web-based projects are listed on a separate page. A list of completed or published papers is also available. The papers here are mostly incomplete, or are else "odd-ball" pieces that will probably never make it to a traditional publisher.

Preprints or web-versions of papers are available for some documents listed here, in various formats. If you have any difficulties getting a copy of something that is not here, please get in touch with me to see if I can help further.

I would of course be most grateful for any comments on these papers. Please note that all material here is copyright. I grant you permission to make one copy for your own personal use.

  1. The model theory of the standard cut by Richard Kaye, Roman Kossak and Tin Lok Wong. (Provisional title.) Work in progress.
  2. Self-embeddings of models of arithmetic. Work in progress.
  3. Nonstandard finite abelian groups by Richard Kaye and Alan Reading. Work in progress.
  4. Counting external sets over a model of arithmetic by Richard Kaye and Alan Reading. Work in progress.
  5. A diophantine undecidable subsystem of arithmetic with no induction axioms Unpublished. Version available here.
  6. Reflective Permutation groups, University of Birmingham Mathematics Preprint 96/11, 1996.
  7. Order-types of models of Peano arithmetic: a short survey, by Andrey Bovykin and Richard Kaye, 14th June 2001. A survey of results on order-types of models of Peano arithmetic! Available in pdf format here.
  8. Arithmetic and the Incompleteness Theorems, 12th August 2000. (Incomplete.) Draft of a paper for the History of Logic, available in pdf format here. A (rather small) part of it is as yet unfinished. I would be very interested to hear any remarks concerning this paper with a view to incorporating them into the final version of the paper. Please email me your comments!
  9. Infinite minesweeper is Turing complete, 13th August 2000. A sequel to `Minesweeper is NP-complete', showing that some straightforward modifications to the minesweeper game yields a system that can simulate arbitrary computations, is available here in pdf format.
  10. Right-orderability of groups, December 18th, 1998. Available in pdf format. This paper gives a minature logical calculus---including the completeness and soundness theorems for it---which characterize those groups that can be right-ordered. It was a precursor to "The Mathematics of Logic".
  11. Reflective permutation groups. April 10th, 1997. Available in postscript format. This paper explores certain properties of permutation groups associated with automorphism groups of recursively saturated structures, and gives some new examples of such groups.
  12. Polish groups, June 26th, 1996. Notes from a study day in model theory and topological groups in Birmingham University, 1995. (Incomplete.) Available in postscript format. Starts from basics, and assumes no prior knowledge of topological groups. The notes focus on Polish groups (topological groups where the topology is metrizable, complete and separable), with a discussion of the small index property. However there is quite a lot of material on more general topological groups to set the scene. Although they were originally intended for the study day in 1995, I have added material since, and the latest version is dated June 1996. They are still not in any way complete, but may still be of use.

List of papers

List of books and other more substantial publications

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