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 Is the smallest $L_\alpha$ with undefinable ordinals always countable?
Miha, you should post your comment as an answer.
Comment by Joel David Hamkins on Forcing CH but not adding $\omega_1$-sequences
The OP didn't say that $M$ has $\neg$CH, although I suppose that would be the main case. What the argument shows is that CH is equivalent to the assertion that there is a forcing notion forcing CH without adding new $\omega_1$-sequences. Indeed, forcing has nothing to do with it. For any model $M$, there is […]
Comment by Joel David Hamkins on Forcing CH but not adding $\omega_1$-sequences
My opinion is that any question about forcing is on-topic on MO.
Comment by Joel David Hamkins on Is there a known Turing machine which halts if and only if the Collatz conjecture has a counterexample?
It may also be helpful to consider also the program that searches for a proof (in ZFC, say, or whatever your favorite strong theory is) that CC is false. We can easily design such a program. It follows that this particular program halts if and ony if there is provably a counterexample to CC. If […]
Comment by Joel David Hamkins on Is there a known Turing machine which halts if and only if the Collatz conjecture has a counterexample?
Perhaps this answer and discussion help explain the point I am trying to make: mathoverflow.net/a/48031/1946.
Comment by Joel David Hamkins on Is there a known Turing machine which halts if and only if the Collatz conjecture has a counterexample?
Yes, I had seen what you wrote. The "always halt" program is one single program, and we already know of it. And the "never halt" program is one single program, and we already know of it. And depending on whether the Collatz conjecture is true or false, therefore, exactly one of these is a single […]
Comment by Joel David Hamkins on Is there a known Turing machine which halts if and only if the Collatz conjecture has a counterexample?
Meanwhile, I don't find the issue pedantic, since as I mentioned, this is unfortunately a very common mistake which leads to many confusions, and I find it important to get it right. I view it as fundamentally similar to the kind of mistake that beginners make in complexity theory by asking about the complexity of […]
Comment by Joel David Hamkins on Is there a known Turing machine which halts if and only if the Collatz conjecture has a counterexample?
Gerhard, yes, I saw the edit in the question, but it still doesn't mention any theory, which I find to be the crux of the foundational confusions here, and also, the "always halt" program is one specific program, as is the "never halt" program. Also, if one is just asking for an equivalence, then the […]

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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Huge Julian Barathieu

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