Stable bimetric theories

ω-Stable Theories: Introduction

1 ω Stable/Totally Transcendental Theories Throughout let T be a complete theory in a countable language L having infinite models. For an L-structure M and A ⊆ M let SM n (A) denote the set of n-types of A. We define a topology (called Stone topology) on SM n (A) by setting basic open sets to be of the form Uφ = {p ∈ SM n (A) : φ ∈ p} where φ is an L(A)-formula. Then SM n (A) is totally disconn...

No consistent bimetric gravity?

Two-tensor, bimetric (or ‘‘f-g’’) gravity (BMG) was born as the fusion of the strong-interaction resonances of the 1960s (specifically that of a massive spin 2 field) with general relativity’s (GR) massless metric [1]. The idea was to join the two symmetrically by giving each its own Einstein-Hilbert action, then coupling the two resulting ‘‘spaces’’ through a nonderivative ‘‘mass term’’ that n...

Countable Models of Stable Theories

The notion of a normal theory is introduced, and it is proved that for such a theory T, /(N„, 7") = 1 or 3e S(l. Wc also include a short proof of Lachlan's theorem that for superstable 7". /(X0, 7") = 1 or > N(1. (The property of normality is stronger than stability but incomparable to superstability.) 1. Preliminaries. We consider here theories T which are countable and complete (and of course...

Translations, Endomorphisms, and Stable Equational Theories

Equational theories of an algebra, i.e. the equivalence relation closed under translations and endomorphisms, are formalized. The correspondence between equational theories and term rewriting systems is discussed in the paper. We get as the main result that any pair of elements of an algebra belongs to the equational theory generated by a set A of axioms iff the elements are convertible w.r.t. ...

Stable Theories with A New Predicate