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 How much high iterative partitioning of the first inaccessible stage can be?
Well, you are referring throughout to "size $V_\kappa$", but this just means "size $\kappa$", and so your way of stating the problem is needlessly cumbersome.
Comment by Joel David Hamkins on Proving independence with large cardinals?
Also, we have no tools to prove instances of nonlinearity in consistency strength.
Comment by Joel David Hamkins on How much high iterative partitioning of the first inaccessible stage can be?
If $\kappa$ is inaccessible, then it is a $\beth$-fixed point, and so $V_\kappa$ has size $\kappa$.
Comment by Joel David Hamkins on Model theory of the complex numbers with conjugation
Ah, you are right. I have edited.
Answer by Joel David Hamkins for Source on smooth equivalence relations under continuous reducibility?
This is more of a comment than an answer, since it is not a perfect fit. But I just thought I would mention the following paper, which is concerned not with continuous reducibility, but computable reducibility. Coskey, Amuel; Hamkins, Joel David; Miller, Russell, The hierarchy of equivalence relations on the natural numbers under computable reducibility, […]
Answer by Joel David Hamkins for Model theory of the complex numbers with conjugation
It is a decidable theory, because it is interpretable in the real-closed field $\langle\mathbb{R},+,\cdot,0,1\rangle$, which has a decidable theory. We can interpret complex numbers $a+bi$ as pairs of real numbers $(a,b)$, and the complex structure, including conjugation, is definable in the reals. (Indeed, this is easily seen to be a bi-interpretation, since we can define […]
Comment by Joel David Hamkins on Relation between $\eta$ and $\omega^L_1$
Well, certainly the oracle concept is natural, and people have studied it. I don't understand what the question is that you might have, but if you do ask it, it should be a separate question.
Comment by Joel David Hamkins on Relation between $\eta$ and $\omega^L_1$
Your comment is related to ordinal register machines, and you seem to be describing some mixture of ordinal tape+register machines. I don't find that a compelling model, given that we have the other models, and they are known to be equi-powerful in various senses. If you want to use ordinal registers, use a register machine. […]

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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