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Sadie Kaye

Dr.

Accepting PhD Students

PhD projects

Richard Kaye’s research is centred on the topic of nonstandard models - systems of numbers behaving like normal numbers but which include infinite and infinitesimal. Study of these models is often combined with other disciplines, including complexity theory, recursion theory, set theory, algebra and analysis.

Dr Kaye is interested in supervising doctoral researchers in the following areas:

Nonstandard models of Peano arithmetic
Recursively saturated models of arithmetic and of other theories
Applications of nonstandard models to other areas of mathematics, especially algebra and group theory
Combinatorial game theory and nonstandard models
Satisfaction classes and notions of truth over a nonstandard model of arithmetic

20022015

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  • 2015

    The model theory of generic cuts

    Kaye, R. & Wong, T. L., 19 Jan 2015, Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. Hirvonen, Å., Kontinen, J., Kossak, R. & Villaveces, A. (eds.). De Gruyter, p. 281-296 (Ontos Mathematical Logic; vol. 5).

    Research output: Chapter in Book/Report/Conference proceeding › Conference contribution