Equality in first-order logic is represented in the language by means of a logical symbol and so it is interpreted uniformly; the semantics says that its interpretation in any structure is the identity relation. This is the absolute notion of identity however, and in fact the only one deserving this name. But there is a related relation: the relation of indiscernibility. Given a structure for a...

Extending a result of Borodin, et. al. [l], we show that any branching program using linear queries " rhixi: c " to sort n numibers i ⌧pp l **,⌧n must satisfy the time-space tradeoff relation TS = n(n*) , The same relation is also shown to be true for branching programs that uses queries " min R = ? " where R is any subset of {xl,x2,...,xnj .

The physical processes that define the spine of the galaxy cluster X-ray luminosity–temperature (L–T) relation are investigated using a large hydrodynamical simulation of the universe. This simulation models the same volume and phases as the millennium simulation and has a linear extent of 500 h Mpc. We demonstrate that mergers typically boost a cluster along but also slightly below the L–T rel...

model theory S. Feferman and J. Barwise (eds.) (1985), ModelTheoretic Logics. Abstract model theory deals with properties of model-theoretic logics L, specified by an abstract syntaxi.e. a set of “sentences” satisfying suitable closure conditionsand “satisfaction” relation M |= φ for φ a sentence of L. With each such L is associated its collection of Elementary Classes, ECL, and from that its...

It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arb...

In this paper a binary relation between L-sets, called attachment, is defined by means of a suitable family of completely coprime filters in L. Examples are given using several kinds of lattice-ordered algebras and a class of attachments is determined whose elements generalize Pu-Liu’s quasi-coincidence relation. Mapping any L-set on X to the set of the attached L-points one gets a frame map fr...

We investigate how L uscher's relation between the nite-volume energy of two pions at rest and pion scattering lengths has to be modiied in quenched QCD. We nd that this relation changes drastically, and in particular, that \enhanced nite-volume corrections" of order L 0 = 1 and L 2 occur at one loop (L is the linear size of the box), due to the special properties of the 0 in the quenched appro...

We introduce a modal language L which is obtained from standard modal logic by adding the Boolean operators on accessibility relations, the identity relation, and the converse of relations. It is proved that L has the same expressive power as the two-variable fragment FO of first-order logic, but speaks less succinctly about relational structures: if the number of relations is bounded, then L-s...

Velocity dispersion σ, radius R and luminosity L of elliptical galaxies are known to be related, leaving only two degrees of freedom and defining the so-called “fundamental plane”. In this Letter we present observational evidence that rich galaxy clusters exhibit a similar behaviour. Assuming a relation L ∝ Rασ2β, the best-fit values of α and β are very close to those defined by galaxies. The d...