Related papers: Hierarchical Multiverse of Sets
The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the…
We develop an untyped framework for the multiverse of set theory. $\mathsf{ZF}$ is extended with semantically motivated axioms utilizing the new symbols $\mathsf{Uni}(\mathcal{U})$ and $\mathsf{Mod}(\mathcal{U, \sigma})$, expressing that…
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
This paper contains analysis of creation of sets and multisets as an approach for modeling of some aspects of human thinking. The creation of sets is considered within constructive object-oriented version of set theory (COOST), from…
Through case studies, we demonstrate how multiverse analysis can strengthen the robustness and transparency of computational social science findings against alternative methodological decisions. We conduct multiverse analyses of three…
Hilary Putnam once suggested that "the actual existence of sets as 'intangible objects' suffers... from a generalization of a problem first pointed out by Paul Benacerraf... are sets a kind of function or are functions a sort of set?"…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems…
This paper will focus on the process of 'fusing' several observations or models of uncertainty into a single resultant model. Many existing approaches to fusion use subjective quantities such as 'strengths of belief' and process these…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in…
In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…
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.…
I shall explore various senses in which ultrafinitism can be fruitfully understood as engaging with a potentialist perspective in mathematics. First, I explain that every model $M$ of the theory of finite arithmetic -- arithmetic with a…
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…
The multiple realizability thesis holds that psychological states may be implemented in a diversity of physical systems. The deep learning revolution seems to be bringing this possibility to life, offering the most plausible examples of…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
Adding interpretability to multivariate methods creates a powerful synergy for exploring complex physical systems with higher order correlations while bringing about a degree of clarity in the underlying dynamics of the system.