2 6 N ov 1 99 7 What internal set theory knows about standard sets

X iv : g r - qc / 9 81 10 53 v 1 1 7 N ov 1 99 8 The internal description of a causal set : What the universe looks like from the inside

We describe an algebraic way to code the causal information of a discrete spacetime. The causal set C is transformed to a description in terms of the causal pasts of the events in C. This is done by an evolving set, a functor which to each event of C assigns its causal past. Evolving sets obey a Heyting algebra which is characterised by a non-standard notion of complement. Conclusions about the...

ar X iv : h ep - p h / 97 10 46 8 v 2 1 2 N ov 1 99 7 Connections Between Lattice Gauge Theory and Chiral Perturbation Theory

In this talk, I address the comparison between results from lattice QCD computations and Chiral Perturbation Theory (ChPT). I briefly discuss how ChPT can be adapted to the much-used quenched approximation and what it tells us about the special role of the η ′ in the quenched theory. I then review lattice results for some quantities (the pion mass, pion scattering lengths and the K + → π + π 0 ...

Internal Set Theory: a New Approach to Nonstandard Analysis

1. Internal set theory. We present here a new approach to Abraham Robinson's nonstandard analysis [10] with the aim of making these powerful methods readily available to the working mathematician. This approach to nonstandard analysis is based on a theory which we call internal set theory (1ST). We start with axiomatic set theory, say ZFC (Zermelo-Fraenkel set theory with the axiom of choice [1...

ar X iv : h ep - p h / 97 11 49 1 v 1 2 7 N ov 1 99 7 Masses of Quarks and Leptons and Mixing Angles in Anti - GUT Theory

We describe a fit to the charged fermion mass hierarchy using the chiral quantum numbers of the maximal anti-grand unification group SM G 3 ×U (1) f , where SM G ≡ SU (3) × SU (2) × U (1). This fit suggests a set of Higgs fields responsible for the breakdown, near the Planck scale, of SM G 3 × U (1) f to the Standard Model group.

N ov 1 99 8 Area Minimizing Sets Subject to a Volume Constraint in a Convex Set