Joel David Hamkins

mathematics and philosophy of the infinite

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Tag Archives: NWO

Modal logics in set theory, NWO grants, 2006 – 2008

Posted on April 30, 2006 by Joel David Hamkins

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Modal logics in set theory, (with Benedikt Löwe), Nederlandse Organisatie voor Wetenschappelijk (B 62-619), 2006-2008.

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Posted in Grants and Awards | Tagged Amsterdam, NWO | Leave a reply

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Joel David Hamkins on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018
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Joel David Hamkins on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018
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Comment by Joel David Hamkins on Naming in math: from red herrings to very long names
A similar point can be raised with respect to unnecessary notation, used to express relations that can be easily expressed in ordinary language.
Answer by Joel David Hamkins for Naming in math: from red herrings to very long names
Let me mention as a counterpoint that there is less need for new terminology than one might expect. Mathematical exposition is often more successful and clearer without new terminology, and one should consider whether one needs any new terminology at all. It seems to be a typical beginner's mistake to name everything in sight, introducing […]
Comment by Joel David Hamkins on Is there any research on set theory without extensionality axiom?
@MikeShulman No, I don't quite know the full extent of this phenomenon, and it is something that I have been wanting to understand much more fully.
Comment by Joel David Hamkins on Combinatorial games with infinite paths, and generalized Sprague-Grundy theory
It seems you are not interested in the larger possibilities offered by infinite play, which are extremely fascinating. Meanwhile, your context of normal play does allow for arbitrary clopen games, however, which never have draws, and I'm not sure the extent to which the Sprague Gundy analysis extends into that realm. Perhaps that would be […]
Comment by Joel David Hamkins on Combinatorial games with infinite paths, and generalized Sprague-Grundy theory
Finite degree is a limitation on the number of moves for a player at each turn, but these set-theoretic issues even with games on $\{0,1\}$, where each player has only two moves.
Comment by Joel David Hamkins on Combinatorial games with infinite paths, and generalized Sprague-Grundy theory
Yes, my answer is that in the general context of infinite play, then for games on countable graphs, even with finite degree, the analysis becomes completely set-theoretic, and quickly things become totally unlike the case of combinatorial game theory. The simplest case of the new realm may be clopen games, which are games that all […]
Answer by Joel David Hamkins for Combinatorial games with infinite paths, and generalized Sprague-Grundy theory
I am not sure what you imagine, but once one makes the move to games with infinite play, then various set-theoretic issues come to light, and the subject becomes more set-theoretic and less like combinatorial game theory. The keyword is determinacy, and there is a very rich literature. A Gale-Stewart game is a game allowing […]
Comment by Joel David Hamkins on Has incorrect notation ever led to a mistaken proof?
@DanielMcLaury There is variant usage. Logicians commonly say that there can be different axiomatizations of the same theory, and under this terminology, a theory is any set of sentences that is closed under logical consequence. Alternatively, logicians allow arbitrary sets of sentences, but in this kind of usage, theories are typically considered only up to […]

New York Logic

Title TBA
Resource Sharing Linear Logic, I
Sub-Kripkean epistemic models I
Generic logical semantics of justifications III
Generic logical semantics of justifications II
Generic logical semantics of justifications.
Cut Elimination
Functors and infinitary interpretations of structures
Recursive Reducts of PA III
Kripke completeness of strictly positive modal logics and related problems

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