Related papers: The uniqueness of the core model
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving…
We show that every Jonsson cardinal is Ramsey in the Steel core model, provided that this model exists and there is no model with a Woodin cardinal. This basic result is improved in two directions. First, we prove the same result for…
In singular models, the optimal set of parameters forms an analytic set with singularities and classical statistical inference cannot be applied to such models. This is significant for deep learning as neural networks are singular and thus…
We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
Structural parameter identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. One of the standard approaches to assessing this…
We study definable J-sets for definable groups and compare them with weakly generic sets. We show that the property that J-sets coincide with weakly generic sets is invariant on enough saturated models, and hence a model-theoretical…
The global approach to control systems which we have been pursuing in other work favours the study of dynamics achievable through control. It employs certain globally defined geometric objects and attempts to describe them in the general…
Self-assembly processes are widespread in nature, and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the…
Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…
Recently, the field of machine learning has undergone a transition from model-centric to data-centric. The advancements in diverse learning tasks have been propelled by the accumulation of more extensive datasets, subsequently facilitating…
Geometrical stability theory is a powerful set of model-theoretic tools that can lead to structural results on models of a simple first-order theory. Typical results offer a characterization of the groups definable in a model of the theory.…
We characterize those standard models M of ZFC which are embeddable, as the class of all standard sets, in a model of internal set theory IST. The necessary and sufficient condition is that 1) there is a wellordering < of M which does not…
Mathematical models are increasingly being used to understand complex biochemical systems, to analyze experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to…
In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some…
The flow models of complex network system are developed and main flow characteristics of its elements are defined. Those characteristics are applied for determining actual structure of the system, analyzing its development on all lifecycle…
The aim of this note is to provide a conceptually simple demonstration of the fact that repetitive model sets are characterized as the repetitive Meyer sets with an almost automorphic associated dynamical system.
Heterogeneous k-core percolation is an extension of a percolation model which has interesting applications to the resilience of networks under random damage. In this model, the notion of node robustness is local, instead of global as in…