AMBIGUITIES IN THE GRAVITATIONAL CORRECTION OF QUANTUM ELECTRODYNAMICS

We verify that quadratic divergences stemming from gravitational corrections to quantum electrodynamics (QED) which have been conjectured to lead to asymptotic freedom near Planck scale are arbitrary (regularization dependent) and compatible with zero. Moreover, we explicitly show that such arbitrary term contributes to the beta function of QED in a gauge dependent way in the gravitational sector.

Interest Rate Volatility Prior to Monetary Union under Alternative Pre-Switch Regimes

The volatility of interest rates is relevant for many financial applications. Under realistic assumptions the term structure of interest rate differentials provides an important predictor of the term structure of interest rates. This paper derives the term structure of differentials in a situation in which two open economies plan to enter a monetary union in the future. Two systems of floating exchange rates prior to the union are considered, namely a free-float and a managed-float regime. The volatility processes of arbitrary-term differentials under the respective pre-switch arrangements are compared. The paper elaborates the singularity of extremely short-term (i.e. instantaneous) interest rates under extensive leaning-against-the-wind interventions and discusses policy issues.

A filter model for mobile processes

This paper presents a filter model for π-calculus and shows its full abstraction with respect to a ‘may’ operational semantics. The model is introduced in the form of a type assignment system. Types are related by a preorder that mimics the operational behaviour of terms. A subject expansion theorem holds. Terms are interpreted as filters of types: this interpretation is compositional. The proof of full abstraction relies on a notion of realizability of types and on the construction of terms, which test when an arbitrary term has a fixed type.

Some consistency proofs and a characterization of inconsistency proofs in illative combinatory logic

It is well known that combinatory logic with unrestricted introduction and elimination rules for implication is inconsistent in the strong sense that an arbitrary term Y is provable. The simplest proof of this, now usually called Curry's paradox, involves for an arbitrary term Y, a term X defined by X = Y(CPy).The fact that X = PXY = X ⊃ Y is an essential part of the proof.The paradox can be avoided by placing restrictions on the implication introduction rule or on the axioms from which it can be proved.In this paper we determine the forms that must be taken by inconsistency proofs of systems of propositional calculus based on combinatory logic, with arbitrary restrictions on both the introduction and elimination rules for the connectives. Generally such a proof will involve terms without normal form and cut formulas, i.e. formulas formed by an introduction rule that are immediately removed by an elimination with at most some equality steps intervening. (Such a sequence of steps we call a “cut”.)The above applies not only to the strong form of inconsistency defined above, but also to the weak form of inconsistency defined by: all propositions are provable, if this can be represented in the system.Any inconsistency proof of this kind of system can be reduced to one where the major premise of the elimination rule involved in the cut and its deduction must also appear in the deduction of the minor premise involved in the cut.We can, using this characterization of inconsistency proofs, put appropriate restrictions on certain introduction rules so that the systems, including a full classical propositional one, become provably consistent.