Related papers: The Future of Set Theory
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
In this paper, we discuss a potential agenda for future work in the theory of random sets and belief functions, touching upon a number of focal issues: the development of a fully-fledged theory of statistical reasoning with random sets,…
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…
After a very brief review of twentieth century elementary particle physics, prospects for the next century are discussed. First and most important are technological limits of opportunities; next, the future experimental program, and finally…
Information theory is rapidly approaching its 70th birthday. What are promising future directions for research in information theory? Where will information theory be having the most impact in 10-20 years? What new and emerging areas are…
The mood at this conference is summarized in David Hughes' comment, ``this decade will be amazing.'' We've just had a pretty good ten years of advances in cosmology and extragalactic astronomy; why should we expect a repeat, another decade…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
Mathematicians still use Naive Set Theory when generating sets without danger of producing any contradiction. Therefore their working method can be considered as a consistent inference system with an experience of over 100 years. My…
As the title of this symposium implies, one of the aims is to examine the future of astrometry as we move from an era in which thanks to the Hipparcos Catalogue everyone has become familiar with milliarcsecond astrometry to an era in which…
The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are…
Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In this article, I demonstrate that this assumption is incorrect. I show that the fundamental physical question of whether a theory is…
This summary talk reviews the LHC 2003 Symposium, focusing on expectations as we prepare to leap over the current energy frontier into new territory. We may learn from what happened in the two most recent examples of leaping into new energy…
Recommender systems are designed to help users in situations of information overload. In recent years, we observed increased interest in session-based recommendation scenarios, where the problem is to make item suggestions to users based…
This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…
Choices in the semantics and the signature of a theory are integral in determining how the theory is used and how challenging it is to reason over it. Our interest in this paper lies in the SMT theory of sequences. Various versions of it…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
Today's lectures are often talks following a straight line of slides. In many lectures the process of content teaching is not as efficient as it could be. Technologies, such as smart-phones and wireless communication, enable a new level of…
In this article we present the prototype of a workshop on naive set theory designed for high school students in or around the seventh year of primary education. Our concept is based on two events which the author organized in 2006 and 2010…
A summary is presented of a symposium held to review recent progress in X-ray astronomy and to discuss prospects for the next generation of X-ray missions. The summary is organized around ten general, astrophysical questions that may…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.