Related papers: Paradigms-Shift in Set Theory
This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…
We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This…
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.…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
Prompting schemes such as Chain of Thought, Tree of Thoughts, and Graph of Thoughts can significantly enhance the reasoning capabilities of large language models. However, most existing schemes require users to define static,…
This is an introduction to the microscopic techniques of non-rational bulk and boundary conformal field theory which are needed to describe strings moving in non-compact curved backgrounds. The latter arise e.g. in the context of…
Neural machine translation (NMT) systems have been shown to give undesirable translation when a small change is made in the source sentence. In this paper, we study the behaviour of NMT systems when multiple changes are made to the source…
Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose…
Recent studies using four-point correlations suggest a parity violation in the galaxy distribution, though the significance of these detections is sensitive to the choice of simulation used to model the noise properties of the galaxy…
We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to…
We propose a new Perturbation Theory framework that can be used to help with the projective solution of the Schr\"odinger equation for arbitrary wavefunctions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our…
In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in $D = 4$ space-time dimensions. We show that such a symmetry-breaking indeed occurs in…
We present a self-contained analysis of infinity from two mathematical perspectives: set theory and algebra. We begin with cardinal and ordinal numbers, examining deep questions such as the continuum hypothesis, along with foundational…
Motivated by Zadeh's paradigm of computing with words rather than numbers, several formal models of computing with words have recently been proposed. These models are based on automata and thus are not well-suited for concurrent computing.…
This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize…
Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity,…
This paper examines the category theory of stratified set theory (NF and KF). We work out the properties of the relevant categories of sets, and introduce a functorial analogue to Specker's T-operation. Such a development leads one to…
Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of…
The next generation of autonomous agents must not only learn efficiently but also act reliably and adapt their behavior in open worlds. Standard approaches typically assume fixed tasks and environments with little or no novelty, which…