Joel David Hamkins

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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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Comment by Joel David Hamkins on In the two-person Killing the Hydra game, what is the winning strategy?
Great! This is excellent. For those readers who might benefit, here is an accessible account of transfinite Nim that I wrote on my blog a few years back: jdh.hamkins.org/transfinite-nim.
Comment by Joel David Hamkins on Does every cofinal branch through Kleene's O compute true arithmetic?
Thanks very much! Here is the DOI for the JSL version: doi.org/10.2178/jsl/1082418544
Comment by Joel David Hamkins on In the two-person Killing the Hydra game, what is the winning strategy?
@NoahSchweber I'd love to hear more, if you can prove this. Meanwhile, I've described what I view as the standard Hydra rule set, and I don't know who wins.
In the two-person Killing the Hydra game, what is the winning strategy?
My question is which player has a winning strategy in the two-player version of the Killing the Hydra game? In their amazing paper, Kirby, Laurie; Paris, Jeff, Accessible independence results for Peano arithmetic, Bull. Lond. Math. Soc. 14, 285-293 (1982), ZBL0501.03017, Laurie Kirby and Jeff Paris introduced the Killing the Hydra game, in which one […]
Comment by Joel David Hamkins on Does every cofinal branch through Kleene's O compute true arithmetic?
Yes, Andreas @AndreasBlass, I agree completely. This was the main reason to think that the Turing degree of the cofinal paths should be high. But I don't see how to reduce the hyperarithmetic reduction to Turing reduction.
Comment by Joel David Hamkins on Does every cofinal branch through Kleene's O compute true arithmetic?
More specifically, my idea about type 1 and type 2 is that we will stick on another $\omega$ many terms (by powers of $2$) and then include the index $3\cdot 5^e$, where $e$ is a program that is recognizably of the form (1) wait for $p$ to halt, then climb through that $\omega$ tower, or […]
Comment by Joel David Hamkins on Does every cofinal branch through Kleene's O compute true arithmetic?
@NoahSchweber I can prove that the generic path you describe must at least compute the halting problem. The reason is that for any program p it is dense to include an index either of type 1 or type 2, where the type 1 index works only if p halts and the index of type 2 […]
Comment by Joel David Hamkins on Does every cofinal branch through Kleene's O compute true arithmetic?
Perhaps we can use that all bounded initial segments of the branch are uniformly c.e. That is, for each n in z, we can enumerate $z\upharpoonright n$.

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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