Related papers: Toward classification theory of good lambda frames…
We study the problem of extending an abstract independence notion for types of singletons (what Shelah calls a good frame) to longer types. Working in the framework of tame abstract elementary classes, we show that good frames can always be…
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…
Robustness and generalization ability of machine learning models are of utmost importance in various application domains. There is a wide interest in efficient ways to analyze those properties. One important direction is to analyze…
In this paper we consider the K-theory of smooth algebraic stacks, establish lambda and gamma operations, and show that the higher K-theory of such stacks is always a pre-lambda-ring, and is a lambda-ring if every coherent sheaf is the…
Recent text and image foundation models are incredibly impressive, and these models are attracting an ever-increasing portion of research resources. In this position piece we aim to shift the ML research community's priorities ever so…
Let $O$ be the ring of power series in one variable over a finite field, with $K$ its fraction field. We introduce the notion of a "formal $K$-vector space"; this is a certain kind of $K$-vector space object in the category of formal…
We continue the work of [KlSh:362] and prove that for lambda successor, a lambda-categorical theory T in L_{kappa^*, omega} is mu-categorical for every mu, mu <= lambda which is above the (2^{LS(T)})^+-beth cardinal.
Our "long term and large scale" aim is to characterize the first order theories T (at least the countable ones) such that: for every ordinal alpha there lambda,M_1,M_2 such that M_1,M_2 are non-isomorphic models of T of cardinality lambda…
We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications…
We develop a stable analogue to the theory of cosimplicial frames in model cagegories; this is used to enrich all homotopy categories of stable model categories over the usual stable homotopy category and to give a different description of…
If cf(kappa) = kappa, kappa^+< cf(lambda) = \lambda, then there is a stationary subset S of {delta<lambda:cf(delta)=kappa} in I[lambda]. Moreover, we can find <C_delta :delta in S>, C_delta a club of lambda, otp(C_delta)=kappa, guessing…
Given a lattice $\Lambda$ in a locally compact abelian group $G$ and a measurable subset $\Omega$ with finite and positive measure, then the set of characters associated to the dual lattice form a frame for $L^2(\Omega)$ if and only if the…
We study the spectrum of limit models assuming the existence of a nicely behaved independence notion. Under reasonable assumptions, we show that all `long' limit models are isomorphic, and all `short' limit models are non-isomorphic.…
We prove the uniqueness of high cofinality limit models in stable abstract elementary classes (AECs) with amalgamation, assuming the existence of a rather weak independence relation. $\textbf{Theorem.}$ Suppose $\mathbf{K}$ is a…
Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal…
We deal with stability theory for ``reasonable'' non-elementary classes without any remanents of compactness (like: above Hanf number or definable by L_{omega_1, omega}).
In the context of a family os scalar-tensor theories with a dynamical $\Lambda$, that is a binomial on the scalar field, the cosmological equations are considered. A general barotropic state equation $p=(\gamma-1)\rho$, for a perfect fluid…
We provide a characterisation of strongly normalising terms of the lambda-mu-calculus by means of a type system that uses intersection and product types. The presence of the latter and a restricted use of the type omega enable us to…
We give the first (ZFC) dividing line in Keisler's order among the unstable theories, specifically among the simple unstable theories. That is, for any infinite cardinal $\lambda$ for which there is $\mu < \lambda \leq 2^\mu$, we construct…
We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this paper we explore stability results in this context. We…