Spectra of Monadic Second-Order Formulas with One Unary Function

We establish the eventual periodicity of the spectrum of any monadic second-order formula where: (i) all relation symbols, except equality, are unary, and (ii) there is only one function symbol and that symbol is unary

Simplicial quantum dynamics

Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups. It radically changes the uncertainty principle for small distances. Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity. Keywords: Quantum logic, quantum set theory, quantum gravity, quantum topology, simplicial quantization.Comment: 25 pages. 1 table. Conference of the International Association for Relativistic Dynamics, Taiwan, 201

On Decidability Properties of Local Sentences

Local (first order) sentences, introduced by Ressayre, enjoy very nice decidability properties, following from some stretching theorems stating some remarkable links between the finite and the infinite model theory of these sentences. We prove here several additional results on local sentences. The first one is a new decidability result in the case of local sentences whose function symbols are at most unary: one can decide, for every regular cardinal k whether a local sentence phi has a model of order type k. Secondly we show that this result can not be extended to the general case. Assuming the consistency of an inaccessible cardinal we prove that the set of local sentences having a model of order type omega_2 is not determined by the axiomatic system ZFC + GCH, where GCH is the generalized continuum hypothesi