This means that for all n ≥ 2, there exists no first-order sentence Fn in the language Ln = (+,−,×,=, 0, 1, In) satisfying the following property: for any real algebraic variety V of R, if we interpret the n-ary predicate In by membership to V then R |= Fn if and only if V is irreducible. Our proof will imply that irreducibility remains undefinable even if we add the exponential function to Ln....

We study the distribution of rational points on a certain exponential-algebraic surface andwe prove, for this surface, a conjecture of A. J. Wilkie. 2000 Mathematics Subject Classification: 11G99, 03C64

Modifying the proof of a theorem of Wilkie, it is shown that if a one dimnsional set S is definable in an O minimal expansion of the ordered field of the reals, and if it is regularly exponentially near to many integral points, then there is an unbounded set, which is R definable without parameters, and which is exponentially near to S.

In this article we will describe some of the main developments in interest-rate modelling since Black & Scholes’ (1973) and Merton’s (1973) original articles on the pricing of equity derivatives. In particular, we will focus on continuoustime, arbitrage-free models for the full term structure of interest rates. Other models which model a limited number of key interest rates or which operate in ...

This paper reassesses the burden of the current U.S. international tax regime and reconsiders well-known welfare benchmarks used to guide international tax reform. Reinventing corporate tax policy requires that international considerations be placed front and center in the debate on how to tax corporate income. A simple framework for assessing current rules suggests a U.S. tax burden on foreign...

The research at University College London School of Medicine (UCLSM) is supported by the Wellcome Trust, Action Research, the Special Trustees of University College Hospital, and the Muscular Dystrophy Group of Great Britain. The studies have been carried out with the assistance of Dr. P. S. Tofts, Mr. D. Delpy and Mr. A. Chu of the Department of Medical Physics (UCLSM), and Mr. N.Taylor of Kin...

System-initiated digressive proposals may be used to introduce new and unexpected information into automated telephone services. These digressions may be viewed as particularly pronounced forms of unsolicited interruptions as they contain information not directly related to the caller’s intended activity. In human–human conversation, interruptions are considered to be speech acts which intrinsi...

In 1981, Paris and Wilkie [28] indicated it was an open question whether IΣ0 would satisfy the Second Incompleteness Theorem for Herbrand deduction. We will show that some specially formulated axiomizations for IΣ0 can evade the Herbrandized version of the Second Incompleteness Theorem.