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Joel David Hamkins

mathematics and philosophy of the infinite

Joel David Hamkins

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Tag Archives: TMWYF

The theory of infinite games, including infinite chess, Talk Math With Your Friends, June 2020

Posted on May 4, 2020 by Joel David Hamkins
2

This will be accessible online talk about infinite chess and other infinite games for the Talk Math With Your Friends seminar, June 18, 2020 4 pm EST (9 pm UK).  Zoom access information.  Please come talk math with me!

Abstract. I will give an introduction to the theory of infinite games, with examples drawn from infinite chess in order to illustrate various concepts, such as the transfinite game value of a position.

Infinite-Chess-TMWYF-2020 Slides.pdfDownload

See more of my posts on infinite chess.

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Posted in Talks, Videos | Tagged game values, games, infinite chess, infinite games, TMWYF | 2 Replies

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Proof and the Art of Mathematics, MIT Press, 2020

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  • Answer by Joel David Hamkins for Modal logic of a bounded Cohen-type frame over a countable model of ZFC + CH
    The modal logic of forcing with iterations of $\newcommand\Add{\text{Add}}\Add(\omega,1)$ and $\Add(\omega,\omega_2)$ is equal to the trivial logic of validities on a three-element linearly ordered frame $\{0,1,2\}$ with $0
  • Comment by Joel David Hamkins on Extracting a first order proof from a non first order proof
    We always have an effective procedure to find a first-order proof by searching through all proofs.
  • Comment by Joel David Hamkins on Do there exist "quasi-decidable" non-trivial properties of Turing Machines?
    Another point is that one might reply to your question by saying: all decidable properties are trivial in virtue of that, and this applies just as much to quasi-decidable, so no, there can be no nontrivial quasi-decidable properties. This is basically how you argued against the falling-off-the-tape result, by saying it was trivial and didn't […]
  • Comment by Joel David Hamkins on Do there exist "quasi-decidable" non-trivial properties of Turing Machines?
    @Benyamin It isn't cheating, since that model of computation is quite standard and appears in many textbooks (it was the model I was taught). But indeed there are a variety of Turing machine models. The paper considers other models, with two-way infinite tape, multiple states marked as halting, etc., and proves similar theorems for them. […]
  • Comment by Joel David Hamkins on Ultralimit versus partial limit
    In my view it is inadvisable to use the symbol $\omega$ in a set-theory context to mean something other than the first infinite ordinal. This invites confusion, and it will cause problems as soon as one wants to refer to the ordinal $\omega$. It's like using $e$ to denote some other real number in a […]
  • Comment by Joel David Hamkins on Infinite hash function $h:\{0,1\}^\omega\to \{0,1\}^*$
    The constant all-zero function seems to fulfill your desired property. Have you asked what you intended?
  • Comment by Joel David Hamkins on Examples of ubiquitous objects that are hard to find?
    @none Yes, that seems to be exactly the same idea.
  • Comment by Joel David Hamkins on Is every nowhere dense closed set contained in the boundary of a regular open set?
    @ChayimLowen I had been worried about both objections, but I see now how the other objection is resolved.

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