The Ontological Import of Adding Proper Classes

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content

Radio pulsar binaries in globular clusters: their orbital eccentricities and stellar interactions

High sensitivity searches of globular clusters (GC) for radio pulsars by improved pulsar search algorithms and sustained pulsar timing observations have so far yielded some 140 pulsars in more than two dozen GCs. The observed distribution of orbital eccentricity and period of binary radio pulsars in GCs have imprints of the past interaction between single pulsars and binary systems or of binary pulsars and single passing non-compact stars. It is seen that GCs have different groups of pulsars. These may have arisen out of exchange or merger of a component of the binary with the incoming star or a "fly-by" in which the original binary remains intact but undergoes a change of eccentricity and orbital period. We consider the genesis of the distribution of pulsars using analytical and computational tools such as STARLAB, which performs numerical scattering experiments with direct N-body integration. Cluster pulsars with intermediate eccentricities can mostly be accounted for by fly-bys whereas those with high eccentricities are likely to be the result of exchanges and/or mergers of single stars with the binary companion of the pulsar, although there are a few objects which do not easily fit into this description. The corresponding distribution for galactic field pulsars shows notable differences from the GC pulsar orbital period and eccentricity distribution. The long orbital period pulsars in the galactic field with frozen out low eccentricities are largely missing from the globular clusters, and we show that ionization of these systems in GCs cannot alone account for the peculiarities.Comment: Accepted for publication in Ap

New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order

In a recent communication Nail Ibragimov introduced the concept of nonlinearly self-adjoint differential equation [N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A: Math. Theor., vol. 44, 432002, 8 pp., (2011)]. In the present communication a nonlinear self-adjoint classification of a general class of fifth-order evolution equation with time dependent coefficients is presented. As a result five subclasses of nonlinearly self-adjoint equations of fifth-order and four subclasses of nonlinearly self-adjoint equations of third-order are obtained. From the Ibragimov's theorem on conservation laws [N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., vol. 333, 311--328, (2007)] conservation laws for some of these equations are established

Calculation of the magnetotransport for a spin-density-wave quantum critical theory in the presence of weak disorder

We compute the Hall angle and the magnetoresistance of the spin-fermion model, which is a successful phenomenological theory to describe the physics of the cuprates and iron-based superconductors within a wide range of doping regimes. We investigate both the role of the spin-fermion interaction that couples the large-momentum antiferromagnetic fluctuations to the so-called "hot-spots" at the Fermi surface and also of an effective higher-order composite operator in the theory. The latter operator provides a scattering mechanism such that the momentum transfer for the fermions close to the Fermi surface can be small. We also include weak disorder that couples to both the bosonic order-parameter field and the fermionic degrees of freedom. Since the quasiparticle excitations were shown in recent works to be destroyed at the "hot-spots" in the low-energy limit of the model, we employ the Mori-Zwanzig memory-matrix approach that permits the evaluation of all transport coefficients without assuming well-defined Landau quasiparticles in the system. We then apply this transport theory to discuss universal metallic-state properties as a function of temperature and magnetic field of the cuprates from the perspective of their fermiology, which turn out to be in qualitative agreement with key experiments in those materials.Comment: 7 pages, 1 figur