Forcing as a computational process, Kobe Set Theory Workshop, March 2021

This was a talk for the Kobe Set Theory Workshop, held on the occasion of Sakaé Fuchino’s retirement, 9-11 March 2021.

Abstract. I shall discuss senses in which set-theoretic forcing can be seen as a computational process on the models of set theory. Given an oracle for the atomic or elementary diagram of a model of set theory $\langle M,\in^M\rangle$, for example, one may in various senses compute $M$-generic filters $G\subset P\in M$ and the corresponding forcing extensions $M[G]$. Meanwhile, no such computational process is functorial, for there must always be isomorphic alternative presentations of the same model of set theory $M$ that lead by the computational process to non-isomorphic forcing extensions $M[G]\not\cong M[G’]$. Indeed, there is no Borel function providing generic filters that is functorial in this sense.

This is joint work with Russell Miller and Kameryn Williams.

Forcing as a computational process

  • J. D. Hamkins, R. Miller, and K. J. Williams, “Forcing as a computational process,” Mathematics arXiv, 2020.
    [Bibtex]
    @ARTICLE{HamkinsMillerWilliams:Forcing-as-a-computational-process,
    author = {Joel David Hamkins and Russell Miller and Kameryn J. Williams},
    title = {Forcing as a computational process},
    journal = {Mathematics arXiv},
    year = {2020},
    volume = {},
    number = {},
    pages = {},
    month = {},
    note = {Under review},
    abstract = {},
    keywords = {under-review},
    source = {},
    doi = {},
    url = {http://jdh.hamkins.org/forcing-as-a-computational-process},
    eprint = {2007.00418},
    archivePrefix = {arXiv},
    primaryClass = {math.LO},
    }

A mathematician’s year in Japan

  • J. D. Hamkins, A Mathematician’s Year in Japan, Amazon Kindle Direct Publishing, 2015, 156 pages.
    [Bibtex]
    @BOOK{Hamkins2015:AMathematiciansYearInJapan,
    author = {Joel David Hamkins},
    title = {A {Mathematician's} {Year} in {Japan}},
    publisher = {Amazon Kindle Direct Publishing},
    year = {2015},
    month = {March},
    keywords = {book},
    url = {http://www.amazon.com/dp/B00U618LM2},
    note = {156 pages},
    }

Years ago, when I was still a junior professor, I had the pleasure to live for a year in Japan, working as a research fellow at Kobe University. During that formative year, I recorded brief moments of my Japanese experience, and every two weeks or so—this was well before the current blogging era—I sent my descriptive missives by email to friends back home. I have now collected together those vignettes of my life in Japan, each a morsel of my experience. The book is now out!


A Mathematician's Year in Japan, by Joel David Hamkins, available on Amazon Kindle BooksA Mathematician’s Year in Japan
Joel David Hamkins

Glimpse into the life of a professor of logic as he fumbles his way through Japan.

A Mathematician’s Year in Japan is a lighthearted, though at times emotional account of how one mathematician finds himself in a place where everything seems unfamiliar, except his beloved research on the nature of infinity, yet even with that he experiences a crisis.

Available on Amazon $4.49.

Please be so kind as to write a review there.
jo eh ru

Kobe University, JSPS Fellowship, 1998

An elegant meal in KobeI held a JSPS Fellowship from the Japan Society for the Promotion of Science at the Graduate School of Kobe University, in Kobe, Japan, from January to December, 1998.  I was a part of the Kobe University Logic Group, and Philip Welch served as my official mentor at that time.  Jörg Brendle started in Kobe at very nearly the same time.