Prof Alex Wilkie - research
My broad research area is Pure Mathematics. Within that I specialise in Mathematical Logic and especially in model theory, which is the semantic side of the subject. I am interested in particular mathematical structures and the functions that occur naturally on them. The main examples are the additive and multiplicative properties of the real and complex numbers together with real analytic and complex holomorphic functions respectively. The aim is to generalise classical elimination theory from the field theoretic (ie additive and multiplicative) setting to the analytic (and even smooth) settings. One of my major successes was to show that all logical properties (ie properties that can be generated from statements about the given functions by use of boolean operations and quantification theory) of the exponential function on the real field can be reduced to purely existential statements. Several applications in maistream mathematics follow from this.
- Mathematical Logic