Related papers: The Future of Set Theory
The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…
Predicting the future is of great interest across many aspects of human activity. Businesses are interested in future trends, traders are interested in future stock prices, and companies are highly interested in future technological…
The first lecture gives a colloquium-level overview of string theory and M-theory. The second lecture surveys various attempts to construct a viable model of particle physics. A recently proposed approach, based on F-theory, is emphasized.
This report summarizes the findings of the DPF Theory Panel which was formed with a goal of understanding the scientific problems and opportunities of the next decade, as well as the challenges involved in sustaining a first-class program…
The process of cognition is analysed to adjust the set theory to physical description. Postulates and basic definitions are revised. The specific sets of predicates, called presets, corresponding to the physical objects identified by an…
A plausible future mathematical claim must satisfy two constraints: it should follow the direction of prior work and respect the formal dependencies that constrain what can validly follow. Existing approaches typically model only one of…
A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
Much of the recent progress in String Theory can be traced to a precise strategy: a careful study of the few models known since the beginnings of the subject, and the abstraction from them of basic properties that one would like to demand…
This writeup is a review of current hot topics on solar neutrinos. It is based on a talk at the conference "Neutrinos: the quest for a new physics scale", held at the CERN on March 2017, where the Organizers entrusted me with a discussion…
Large language models (LLMs) must often respond to highly ambiguous user requests. In such cases, the LLM's best response may be to ask a clarifying question to elicit more information. Existing LLMs often respond by presupposing a single…
We discuss why Type Theory is preferable as foundation of Mathematics compared to set theory.
Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps 'localized', form of 'becoming'. The possibility of fundamental becoming is nourished by the fact that…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…
The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a…
We discuss whether science is in the process of being transformed from a quest for causality to a quest for correlation in light of the recent development in artificial intelligence. We observe that while a blind trust in the most seductive…
The purpose of this brief article is to clarify certain distortions of the history of ideas about the quantum theory of de Sitter space that have appeared in recent literature.
Our lives have been immensely improved by decades of automation research -- we are more comfortable, more productive and safer than ever before. Just imagine a world where familiar automation technologies have failed. In that world,…
Recent highlights from the HERA experiments, Hermes, H1 and ZEUS, are reviewed and ideas for future analyses to fully exploit this unique data set are proposed. This document is a summary of a workshop on future physics with HERA data held…