Richard Kaye's research papers

This page lists research papers (including some web or electronic papers). More substantial publications including books and other major web-based projects are listed on a separate page. Preprints or web-versions of papers are available for some documents listed here. Generally these are papers which haven't yet appeared yet. Some draft documents, or other papers which are not completed yet may be available by following this link.

For copyright reasons, most of the papers listed are not available here. If you have any difficulties getting a copy, please email or write to me to see if I can help further. For some of these publications I have further notes and/or a list of errata. These are available in (La)TeX format or postscript format as indicated. Where the papers are only available in XHTML+MathML format, the instructions for setting up your browser are available HERE.

1. Axiomatizations and quantifier complexity. Originally in the proceedings of the 6th Easter Conference in Model Theory, 1988. Republished here in PDF format.
2. Parameter free induction in arithmetic. Originally in the proceedings of the 5th Easter Conference in Model Theory, 1987. Republished here in PDF format.
3. The arithmetic of cuts in models of arithmetic. Available in PDF format.
4. The model theory of the standard cut By Richard Kaye, Roman Kossak and Tin Lok Wong. Forthcoming.
5. Nonstandard finite abelian groups. By Richard Kaye and Alan Reading. Forthcoming.
6. Amphi-ZF : axioms for Conway games By Michael Cox and Richard Kaye. Submitted. Electronic version of 12th Septemer 2011, in PDF format.
7. The model theory of generic cuts by Richard Kaye and Tin Lok Wong. Submitted. Electronic version of 3rd June 2011, in PDF format.
8. Transplendent models: expansions omitting a type, by Fredrik Engström and Richard Kaye. Accepted. To appear in the Notre Dame Journal of Formal Logic.
9. Tennenbaum's Theorem for Models of Arithmetic. In: Set Theory, Arithmetic, and Foundations of Mathematics Lecture Notes in Logic (No. 36), Edited by Juliette Kennedy (University of Helsinki) and Roman Kossak (City University of New York) (ISBN-13: 9781107008045). Published September 2011.
10. Automorphisms and constructions of models of set theory In: One hundred years of axiomatic set theory. (Ed. Roland Hinnion and Thierry Libert) Cahiers du centre de logique, http://www.logic-center.be/cahiers, volume 17, 2010. ISBN 978-2-87209-974-0. Pages 73-88.
11. On the bounding lemma for KF In: One hundred years of axiomatic set theory. (Ed. Roland Hinnion and Thierry Libert) Cahiers du centre de logique, http://www.logic-center.be/cahiers, volume 17, 2010. ISBN 978-2-87209-974-0. Pages 89-96.
12. Truth in generic cuts by Richard Kaye and Tin Lok Wong. Applied Logic.Annals of Pure and Applied Logic Volume 161, Issue 8, May 2010, Pages 987-1005.
13. Generic cuts in models of arithmetic Mathematical Logic Quarterly, 2008, vol 54, No. 2, 129 DOI 10.1002/malq.200710017.
14. Normal subgroups of nonstandard symmetric and alternating groups, by John Allsup and Richard Kaye, Archive for Mathematical Logic, Febrary 2007, vol 46 number 2, pages 107-121. Further details.
15. Algumas configurações do Minesweeper (Some Minesweeper Configurations) pp 181-189, Boletim Sociedade Portuguesea de Mathemática, Janeiro 2007 (Número especial), Lisbon. ISSN 0872-3672. (English version available here.)
16. On interpretations of arithmetic and set theory. By Richard Kaye and Tin Lok Wong. Notre Dame J. Formal Logic Volume 48, Number 4 (2007), 497-510. On-line versions in several formats available here.
17. The GLOSS system for transformations from plain text to XML. Refereed paper for the Proceedings of MathUI 2006 at http://www.activemath.org/~paul/MathUI06/. Online copy in PDF format at href="http://www.activemath.org/~paul/MathUI06/proceedings/Kaye-gloss-MathUI06.pdf
18. Three papers on GLOSS, XML and MathML. On-line versions (in several formats available here.
19. Why (and how) I am using XML and MathML', MSOR Connections Vol 6 No 1 Feb 2006, 20-22. On-line version available here.
20. Order-types of models of Peano arithmetic, by Andrey Bovykin and Richard Kaye. pp275-285 of: "Logic and Algebra", edited by Yi Zhang with a preface by Oleg Belegradek. Contemporary Mathematics 302, American Mathematical Society, Providence, USA. ISBN 0-8218-2984-X.
21. Minesweeper is NP-complete', Mathematical Intelligencer, 2000. For other papers on Minesweeper, see my list of unpublished and other papers or go to my minesweeper page.
22. On models constructed by means of the arithmetized completeness theorem. By R.W.Kaye and H.Kotlarski. Mathematical Logic Quaterly, 2000.
23. On models constructed by means of the arithmetized completeness theorem. By R.W.Kaye and H.Kotlarski. University of Birmingham School of Mathematics and Statistics preprint number 99/5, February 1999.
24. Review-essay on: C. Smorynski, Logical number theory I (Springer-Verlag). Modern Logic.
25. A diophantine undecidable subsystem of arithmetic with no induction axioms', to appear in the Journal of Symbolic Logic. Preprint available here in postscript format.
26. Diophantine undecidable theories of arithmetic', Collegium Logicum, the Annals of the Kurt G"odel Society, Vienna.
27. Constructing kappa-like models of arithmetic', Journal of the London Mathematical Society (2), 55 (1997) pp 1-10.
28. Minesweeper is NP-complete', University of Birmingham Mathematics Preprint 97/23, 1997.
29. Infinitary definitions of equivalence relations in models of PA', Annals of Pure and Applied Logic, 89 (1997), pp 37-43.
30. Reflective Permutation groups', University of Birmingham Mathematics Preprint 96/11, 1996.
31. Diophantine Undecidable Subsystems of Arithmetic', University of Birmingham Mathematics Preprint 96/13, 1996.
32. The Quantifier Complexity of NF', Bulletin of the Belgian Mathematical Society Simon Stevin, ISSN 1370-1444, 3 (1996), pp 301-312.
33. The theory of kappa-like models of arithmetic', Notre Dame Journal of Formal Logic, Fall 1995, 547--559. Addendum available in LaTeX2e or postscript format.
34. Review of H\'ajek--Pudl\'ak Metamathematics of first-order arithmetic' (published by Springer, 460 pages). The Journal of Symbolic Logic, 60 (1996), 1317--1320.
35. Automorphisms of models of true arithmetic: recognizing some basic open subgroups', by Henryk Kotlarski (Warsaw) and Richard Kaye. Notre Dame J. Formal Logic 35 (winter 1994) 1--14.
36. Indiscernibles', In Kaye and Macpherson (eds) Automorphisms of first-order structures, OUP 1994, 257--279.
37. A Galois correspondence for countable recursively saturated models of Peano arithmetic', In Kaye and Macpherson (eds) Automorphisms of first-order structures, OUP 1994, 293--312.
38. Infinitary definitions of equivalence relations in models of PA', University of Birmingham Mathematics Preprint 94/32.
39. Two papers on $\kappa$-like models of arithmetic', University of Birmingham Mathematics Preprint 94/35.
40. Hilbert's tenth problem for weak theories of arithmetic'. In the proceedings of the conference on Provability, Interpretability and Arithmetic, Utrecht, August 1991. (Annals of Pure and Applied Logic 61 (1993) 63--74).
41. Using Herbrand-type theorems to separate strong fragments of arithmetic'. In the proceedings of the Workshop on Arithmetic, Proof theory, and Complexity, Prague, July 1991 (eds P. Clote and J. Kraj\'\i\v{c}ek). Oxford University Press, 1993.
42. Open induction, Tennenbaum phenomena, and complexity theory'. In the proceedings of the Workshop on Arithmetic, Proof theory, and Complexity, Prague, July 1991 (eds P. Clote and J. Kraj\'\i\v{c}ek). Oxford University Press, 1993.
43. Review-essay on: T.E. Forster, Set theory with a universal set: exploring an untyped universe (OUP, Oxford logic guides). Notre Dame J. Formal Logic 34 (1993) 302--309.
44. The automorphism group of a countable recursively saturated structure'. The Proceedings of the London Math Society 32 (1992) 399--408.
45. Model-theoretic properties characterizing Peano Arithmetic'. The Journal of Symbolic Logic 56 (1991) 949--63.
46. Automorphisms of recursively saturated models of arithmetic', by Kaye, R.W., Kossak, R. and Kotlarski, H. Annals of Pure and Applied Logic 55 (1991) 67--99.
47. On cofinal extensions of models of fragments of arithmetic'. Notre Dame J. Formal Logic 32 (1991) 399--408.
48. End extensions preserving power set', by Forster, T.E. and Kaye, R.W. The Journal of Symbolic Logic 56 (1991) 323--8.
49. A Generalization of Specker's theorem on typical ambiguity'. The Journal of Symbolic Logic 56 (1991) 458--66.
50. Diophantine induction' Annals of Pure and Applied Logic 46 (1990) 1--40.
51. Parameter-free universal induction' Zeitschrift f\"ur Math. Logik (1989) 443--56.
52. On parameter free induction schemas', by Kaye, R. W., Paris, J.B., and Dimitracopoulos, C. The Journal of Symbolic Logic 53 (1988) 1082--97.
53. Axiomatizations and quantifier complexity', in: Proceedings of the 6th Easter Conference on Model Theory, Bernd Dahn and Helmut Wolter (eds), Sektion Mathematik der Humboldt-Universit\"at zu Berlin, 1988, 65--84.

List of books and other more substantial publications