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Joel David Hamkins

mathematics and philosophy of the infinite

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Recent Comments

Nataly on Draw an infinite chessboard in perspective, using straightedge only
Joel David Hamkins on Set-theoretic mereology: the theory of the subset relation is decidable
Joel David Hamkins on A gentle introduction to Boolean-valued model theory
Viktor Kuncak on Set-theoretic mereology: the theory of the subset relation is decidable
Joel David Hamkins on A gentle introduction to Boolean-valued model theory

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Mathoverflow activity

Comment by Joel David Hamkins on Are there strong set theories written in infinitary language, that are finitary FOL complete?
For second-order logic, as opposed to infinitary logic, see related work in arxiv.org/abs/2009.07164
Comment by Joel David Hamkins on MIP*=RE theorem and its impact on logic and proof theory
I don't think the post needs to be CW.
Comment by Joel David Hamkins on Negative of combinatorial game
This is related to what Gro-tsen has answered concerning whether negation and misere game are well-defined.
Comment by Joel David Hamkins on Most 'unintuitive' application of the Axiom of Choice?
I would say that you don't have the theory of Lebesgue measure in that context. You might have a function of some kind that fulfills (one of) the standard definitions of Lebesgue measure, but it won't fulfill other standard definitions, which are no longer equivalent in that theory. What you would have is a pale […]
Comment by Joel David Hamkins on Comparison of model-theoretic and axiomatic approaches to NSA
Ah, sorry, indeed I was thinking of standard sets. I don't know anything really about internal sets, as I rarely work in that framework.
Comment by Joel David Hamkins on Comparison of model-theoretic and axiomatic approaches to NSA
In items 1 and 2, I wonder whether you are exaggerating the difficulty in using the model theoretic approach. For 1, if $A$ is infinite, including a sequence $\langle a_n\rangle_n$ of distinct elements, and then consider $a^*_N$ for some nonstandard $N$. By assumption this is standard, and so by elementarity it must have a standard […]
Comment by Joel David Hamkins on Negative of combinatorial game
Every game can be played as a misère game, and every game is the misère game of another game, so I don't quite understand your question.
Comment by Joel David Hamkins on Negative of combinatorial game
Yes, agreed. I was thinking of it mainly because those are the rules by which misere chess is often played in the club rooms at scholastic chess tournaments I have often attended when my kids were younger.

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