This paper is part of a research programme on the structure of the moduli space of Lorentzian geometries, a Lorentzian analogue of Gromov–Hausdorff theory based on the use of the Lorentz distance as… Expand

We give a covariant definition of closeness between (time-oriented) Lorentzian metrics on a manifold M, using a family of functions which measure the difference in volume form on one hand and, on the… Expand

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov?Hausdorff distance… Expand

We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the… Expand

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In section 2, I work gradually towards a construction of the limit space. I prove that the… Expand

A logically consistent and precise theory of quantum gravity is presented that automatically incoorporates an extended form of gravity as well as a quantum gauge theory and is to a high degree Whiteheadian.Expand

We observe two things in this paper : namely that the Banach Tarski paradox is false and that the correct part of the proof leads to a violation of the axiomof choice.

This work extends the language of mathematics by generalizing the logical implication and negation and serves as an extension of intuitionistic logic.Expand

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance… Expand