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, information about work-in-progress,
or other papers are be available by following this link.
For copyright reasons, some of the papers listed here are not available
by clicking links on this page. If you have any difficulties getting a copy,
please get in touch with me to see
if I can help further. For some of these publications listed here I have further
notes and/or a list of errata. These are available in a number of formats
- Axiomatizations and quantifier complexity.
Originally published in the proceedings of the 6th Easter Conference in
Model Theory,Berlin 1988. Republished here
in PDF format.
- Parameter free induction in arithmetic.
Originally published in the proceedings of the 5th Easter Conference in
Model Theory,Berlin 1987. Republished here
in PDF format.
- The arithmetic of cuts in models of arithmetic.
Submitted. Preliminary version available in PDF format.
- Amphi-ZF: axioms for Conway games by Michael Cox and
Richard Kaye. Archive for Mathematical Logic,
Volume 51 Issue 3-4, May 2012, Pages 353-371.
- The model theory of generic cuts by Richard Kaye and Tin Lok
Wong. Accepted. electronic
version of 3rd June 2011, in PDF format available here.
- Transplendent models: expansions omitting a type by
Fredrik Engström and Richard Kaye. To appear in the Notre
Dame Journal of Formal Logic.
- 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.
- 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.
- 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.
- Truth in generic cuts by Richard Kaye and Tin Lok Wong.
Annals of Pure and Applied Logic Volume 161, Issue 8,
May 2010, Pages 987-1005.
- Generic cuts in models of arithmetic. Mathematical Logic
Quarterly, 2008, vol 54, No. 2, 129 DOI 10.1002/malq.200710017.
- 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.
- Algumas configurações do Minesweeper (Some Minesweeper
Configurations) pp 181-189, Boletim Sociedade Portuguesea de
Mathemática, Janeiro 2007 (Número especial), Lisbon. ISSN
version available here.
- On interpretations of arithmetic and set theory by Richard Kaye
and Tin Lok Wong. Notre Dame Journal of Formal Logic Volume 48, Number 4
(2007), 497-510. On-line versions in several formats
- The GLOSS system for transformations from plain text to
XML. Refereed paper for The
Proceedings of MathUI 2006. An
- Three papers on GLOSS, XML and MathML. On-line versions (in
several formats) available here.
- Why (and how) I am using XML and MathML MSOR
Connections Vol 6 No 1 Feb 2006, 20-22.
On-line version available here.
- 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
- Minesweeper is NP-complete, Mathematical Intelligencer,
2000. For other papers on Minesweeper, see my list
of unpublished and other papers and/or go to
my minesweeper page.
- On models constructed by means of the arithmetized completeness
theorem by R.W.Kaye and H.Kotlarski. Mathematical Logic
- Review-essay on: C. Smorynski, "Logical number theory I"
Modern Logic vol. 8, no. 1-2 (1998-2000) pp154-158.
- Diophantine undecidable theories of arithmetic. Collegium
Logicum, the Annals of the Kurt Gödel Society, vols 3-4, Vienna.
- Constructing kappa-like models of arithmetic, Journal of the
London Mathematical Society (2), 55 (1997) pp 1-10.
- Infinitary definitions of equivalence relations in models of
PA, Annals of Pure and Applied Logic, 89 (1997), pp37-43.
- The Quantifier Complexity of NF, Bulletin of the Belgian
Mathematical Society Simon Stevin, ISSN 1370-1444, 3 (1996),
- 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.
- Review of Hájek–Pudlák "Metamathematics of first-order
arithmetic" (published by Springer, 460 pages). The Journal of
Symbolic Logic, 60 (1996), 1317--1320.
- Automorphisms of models of true arithmetic: recognizing some
basic open subgroups, by Henryk Kotlarski and Richard
Kaye. Notre Dame J. Formal Logic 35 (winter 1994) 1--14.
- Indiscernibles, In Kaye and Macpherson (eds)
Automorphisms of first-order structures, OUP 1994,
- A Galois correspondence for countable recursively saturated
models of Peano arithmetic, In Kaye and Macpherson (eds)
Automorphisms of first-order structures, OUP 1994,
- 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).
- 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. Krajíček). Oxford University Press, 1993.
- 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.
Krajíček). Oxford University Press, 1993.
- 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.
- The automorphism group of a countable recursively saturated
structure. The Proceedings of the London Math Society 32
- Model-theoretic properties characterizing Peano Arithmetic.
The Journal of Symbolic Logic 56 (1991) 949--63.
- 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.
- On cofinal extensions of models of fragments of arithmetic.
Notre Dame J. Formal Logic 32 (1991) 399--408.
- End extensions preserving power set, by Forster, T.E. and Kaye,
R.W. The Journal of Symbolic Logic 56 (1991) 323--8.
- A Generalization of Specker's theorem on typical ambiguity.
The Journal of Symbolic Logic 56 (1991) 458--66.
- Diophantine induction Annals of Pure and Applied Logic
46 (1990) 1--40.
- Parameter-free universal induction Zeitschrift für
Math. Logik (1989) 443--56.
- On parameter free induction schemas, by Kaye, R. W., Paris,
J.B., and Dimitracopoulos, C. The Journal of Symbolic Logic
53 (1988) 1082--97.
List of other papers and work in progress
List of books and other more substantial publications
Back to Richard Kaye's home page