相关论文: The Future of Set Theory

Drawing on infrastructure studies in HCI and CSCW, this paper introduces Protocol Futuring, a methodological framework that extends design futuring by foregrounding protocols -- rules, standards, and coordination mechanisms -- as the…

What will Semantic Web research focus on in 20 years from now? We asked this question to the community and collected their visions in the "Next 20 years" track of ESWC 2023. We challenged the participants to submit "future" research papers,…

Knowing the distance of an astrophysical object is key to understanding it. However, at present, comparisons of theory and observations are hampered by precision (or lack thereof) in distance measurements or estimates. Putting the many…

Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…

We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic.

The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…

These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…

A question is proposed whether or not set theory is consistent.

In this article we wonder what the next 100 years will bring for women in astronomy in the UK. After this year of looking back and celebrating 100 years of women in the Royal Astronomical Society (RAS), we now ask: what might the future…

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…

We here report the development of a structure that shows the proteresis phenomenon in more general setting and set out its philosophical implications. In this case, the questions relate to how we are to interpret what will happen in the…

I offer brief observations on matters discussed at the XIV International Conference on Hadron Spectroscopy and explore prospects for hadron physics.

Several results about the union-closed sets conjecture are presented.

These are lecture notes from a course I gave at the University of Wisconsin during the Spring semester of 1993. Part 1 is concerned with Borel hierarchies. Section 13 contains an unpublished theorem of Fremlin concerning Borel hierarchies…

Making conjectures about future consequences of a technology is an exercise in trying to reduce various forms of uncertainty. Both to produce and reason about these conjectures requires understanding their potential limitations. In other…

In 2007 an international conference engaged a reflection on the present conditions for sciences and scientific practice, to initiate a dialogue between science, philosophy, epistemology and sociology. Starting from many examples taken from…

A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…

When we read, we make predictions about upcoming words; these predictions influence our reading behavior. The success of large language models (LLMs), which, like humans, make predictions about upcoming words, has motivated their use as…

Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…

The International System of Units (SI) is fundamental for the social, and not only the scientific, role of metrology, and as such its understandability is a crucial issue. According to the current draft of the new SI Brochure, the next…