Richard Kaye's Research Interests

Unlike you, I was able to combine mathematical logic with romantic inconsistency...

"Torn Curtain", Hitchcock, 1966.

My research is in Mathematical Logic and I am interested in almost anything related to first-order theories of arithmetic and their models. The theories I am interested in are usually subtheories of Peano Arithmetic (PA), especially PA itself, and also others, such as Presburger arithmetic.

Out of necessity, I am able to read papers in proof-theory (and to use proof-theory in my work), but I much prefer model-theoretic arguments and constructions.

There are close links between models of arithmetic and the general notion of recursive saturation in model theory, and I am very interested in recursively saturated models also. This has lead me to apply methods from nonstandard models of arithmetic and recursive saturation to permutation group theory.

There is an active programme in Birmingham for postgraduate research students in mathematics, and I currently have one research student working on models of arithmetic. There is plenty of scope for further work in this or other areas too. For more information abount my research follow one of the links here.

  1. List of major publications, including books and web-publications
  2. List of research papers, including journal papers, e-papers and others
  3. Further background information on my research, including some backround information for prospective postgradute students and others.

Richard Kaye's home page