Chains of existentially closed models of positive (n1, n2)-Jonsson theories

In this article are considered model - theoretical properties of chains of positive ( n1,n2) - Jonsson theories. Herewith considered theories is perfect in the sense of the existence of appropriate model companion. The main obtained results are as follows: introduced new concepts n 2 - elimination of quantifier for positive theory, ( n1,n2) - Jonsson theory, n1-Jonsson chain; indicated a feature of perfect ( n1,n2) - positive Jonsson theor

Existentially positive Mustafin theories of S-acts over a group

The paper is connected with the study of Jonsson spectrum notion of the fixed class of models of Sacts signature, assuming a group as a monoid of S-acts. The Jonsson spectrum notion is effective when describing theoretical-model properties of algebras classes whose theories admit joint embedding and amalgam properties. It is usually sufficient to consider universal-existential sentences true on models of this class. Up to the present paper, the Jonsson spectrum has tended to deal only with Jonsson theories. The authors of this study define the positive Jonsson spectrum notion, the elements of which can be, non-Jonsson theories. This happens because in the definition of the existentially positive Mustafin theories considered in a given paper involve not only isomorphic embeddings, but also immersions. In this connection, immersions are considered in the definition of amalgam and joint embedding properties. The resulting theories do not necessarily have to be Jonsson. We can observe that the above approach to the Jonsson spectrum study proves to be justified because even in the case of a non-Jonsson theory there exists regular method for finding such Jonsson theory that satisfies previously known notions and results, but that will also be directly related to the existentially positive Mustafin theory in question

Path Integration in Two-Dimensional Toplogical Quantum Field Theory

A positive, diffeomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure, give the two-dimensional axiomatic topological quantum field theories, or TQFT's, in terms of which Durhuus and Jonsson decompose every two-dimensional unitary TQFT as a direct sum.Comment: 13 pages, LaTeX with amsfonts and psfig, 3 postscript figures and .bbl file tar'd and compressed by uufile

The hybrids of the ∆ − PJ theories

When studying Jonsson theories, which are a wide subclass of inductive theories, it becomes necessary to study the so - called Jonsson sets. Similar problems are considered both in model theory and in universal algebra. This topic is related to the study of model - theoretical properties of positive fragments. These fragments are a definable closure of special subsets of the semantic model of a fixed Jonsson theory. In this article are considered model - theoretical properties of a new class of theories, namely ∆ - PJ theories of countable first - order language. These are theories that are obtained from ∆ - PJ theories by replacing in the definition of ∆- PJ theories of morphisms (∆ - continuities) with morphisms (∆ - immersions). A number of results were obtained, ∆ - PJ fragments, ∆ - PJ sets, hybrids of ∆ - PJ theories. All questions considered in this article are relevant in the study of Jonsson theories and their model classes

Properties of a stability for positive Jonsson theories

Actually, we study the connections of the Δ-PM-theories with their centers in the enrich signature. The properties of various companions of some Δ-PM-theories and their connection with this theory are considered on the language of the central types of positive Jonsson theory

On Jonsson varieties and quasivarieties

In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory,  J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closedness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question

On Jonsson varieties and quasivarieties

In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closed ness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question

Direct Sum Decompositions and Indecomposable TQFT's

The decomposition of an arbitrary axiomatic topological quantum field theory or TQFT into indecomposable theories is given. In particular, unitary TQFT's in arbitrary dimensions are shown to decompose into a sum of theories in which the Hilbert space of the sphere is one-dimensional, and indecomposable two-dimensional theories are classified.Comment: 10 pages, AMSLaTeX, 5 figures compressed and uuencoded by uufile

Noncommutative waves have infinite propagation speed

We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there are no conditions on the degree of the nonlinearity provided the potential is positive. We furthermore prove that nonlinear noncommutative waves have infinite propagation speed, i.e., if the initial conditions at time 0 have a compact support then for any positive time the support of the solution can be arbitrarily large.Comment: 15 pages, references adde

Cosmology of the Lifshitz universe

We study the ultraviolet complete non-relativistic theory recently proposed by Horava. After introducing a Lifshitz scalar for a general background, we analyze the cosmology of the model in Lorentzian and Euclidean signature. Vacuum solutions are found and it is argued the existence of non-singular bouncing profiles. We find a general qualitative agreement with both the picture of Causal Dynamical Triangulations and Quantum Einstein Gravity. However, inflation driven by a Lifshitz scalar field on a classical background might not produce a scale-invariant spectrum when the principle of detailed balance is assumed.Comment: 23 pages. v2: one reference and one equation added, main conclusions unchanged; v3: matches published version, discussion improved, typos correcte