Related papers: Superstable theories and representation
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the…
We show that the theory of a non-degenerate representation of a C*-algebra A over a Hilbert space H is superstable. Also, we characterize forking, orthogonality and domination of types and show that the theory has weak elimination of…
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…
We propose a framework for model-theoretic stability and simplicity in an approximate first-order setting and generalize some classical results.
Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a…
We introduce the notion of stable representations, -- it is a new class of the representations of a certain class of groups which defined with positive definite functions which generalize the classical notion of the characters (or trace).…
This paper continues math.LO/0009087. We present a rank function for NSOP_1 theories and give an example of a theory which is NSOP_1 but not simple. We also investigate the connection between maximality in the ordering <^* among complete…
In the first edition of Classification Theory, the second author characterized the stable theories in terms of saturation of ultrapowers. Prior to this theorem, stability had already been defined in terms of counting types, and the unstable…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
A choice of first-order variables for the characteristic problem of the linearized Einstein equations is found which casts the system into manifestly well-posed form. The concept of well-posedness for characteristic problems invoked is that…
We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…
Our aim is to prove that if T is a complete first order theory, which is not superstable (no knowledge on this notion is required), included in a theory T_1 then for any lambda > |T_1| there are 2^lambda models of T_1 such that for any two…
The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from…
We review the main properties of a supersolid. We describe first the macroscopic equation that satisfies a supersolid based on general arguments and symmetries and show that such solids might exhibit simultaneously or independently both…