Causal sets are a particular class of partially ordered sets, which are proposed as basic models of discrete space-time, specially in the field of quantum gravity. In this context, we show the existence of temporal foliations for any causal set, or more generally, for a causal space. Moreover, we show that automorphisms of a large class of infinite causal sets fall into two classes 1) Automorphisms of spacelike hypersurfaces in some given foliation, or 2) Translations in time. More generally, we (...) show that for any automorphism \ of a generic causal set \, there exists a partition of \ into finitely many subcausets, on each of which or above hold. These subcausets can be assumed connected if, in addition, there are enough distinct orbits under \. (shrink)

We prove quantifier elimination for the field ${\Bbb Q}_{p}((t^{{\Bbb Q}}))$ (the completion of the field of Puiseux series over ${\Bbb Q}_{p}$ ) in Macintyre's language together with symbols for functions in a class containing both t-adically and p-adically overconvergent functions. We also show that the theory of ${\Bbb Q}_{p}((t^{{\Bbb Q}}))$ is b-minimal in this language.

In this paper we prove that the field of Logarithmic-Exponential power series endowed with the exponential function and a class of analytic functions containing both the overconvergent functions in the t -adic norm and the usual strictly convergent power series is o-minimal.