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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  • Comment by Joel David Hamkins on An infinite game possibly due to Ernst Specker
    @Richard, the game with an uncountably creative Chocolatier doesn't have that defect---if there are uncountably many chocolate types, then even when only two are served each turn, there can be no winning strategy for the Glutton that doesn't depend on the history.
  • Comment by Joel David Hamkins on Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?
    Thank you very much for this extremely informative answer! Perfect.
  • Comment by Joel David Hamkins on Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?
    Great ! Thanks.
  • Comment by Joel David Hamkins on Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?
    For example, a model of ZFC can think some nonstandard fragment PA_k of PA is consistent, which would provide an interpretation of PA without the model thinking so.
  • Comment by Joel David Hamkins on Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?
    But now I am wondering again about the nonsound case. Why must ZFC prove that the interpretation is a PA interpretation, just because it is? Does this break your argument for the nonsound case?
  • Comment by Joel David Hamkins on Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?
    I don't think it is artificial, and indeed I had similar arguments using the universal algorithm, which I realize now achieve the same result as your answer, but I hadn't put it all together.
  • Comment by Joel David Hamkins on Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?
    For the other side, what seems relevant is that PA$\not\vdash\varphi$ rather than $I\Sigma_1\not\vdash\varphi$.
  • Comment by Joel David Hamkins on Can we interpret arithmetic in set theory, with exactly PA as the ZFC provable consequences?
    Ah, now you have mentioned soundness.

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absoluteness Arthur Apter buttons+switches CH chess computability countable models definability determinacy elementary embeddings equivalence relations forcing forcing axioms games GBC geology ground axiom HOD hypnagogic digraph indestructibility infinitary computability infinite chess infinite games ITTMs Jonas Reitz kids KM large cardinals maximality principle modal logic models of PA multiverse open games ordinals Oxford philosophy of mathematics pluralism potentialism PSC-CUNY supercompact truth universal definition universal program Victoria Gitman W. Hugh Woodin
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