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 Are the cardinals of $G$ and $G/H$ equal?
@YCor If the question were closed/closing, then I would agree that there is no need to post an answer. But if the question remains open, then I believe it is best to answer, even if the answer is not difficult. It is a way of resolving the question, which is a better result for the […]
Comment by Joel David Hamkins on Are the cardinals of $G$ and $G/H$ equal?
@Mizi Why don't you post your answer as an answer? The site works best when people post answers as answers. Your argument shows that we can make $G/H$ any desired compact group we like, and we can make $|G|$ as large as desired.
Comment by Joel David Hamkins on What do you call the generalisation of the direct image?
What you call the "direct" image I would usually call the pointwise image.
Answer by Joel David Hamkins for What do you call the generalisation of the direct image?
This idea is commonly used in set theory with atoms. I'm not sure whether it has a standard name, but I would be inclined to call it the natural extension of $f$ to sets. There is no need to stop the iteration at $\omega$ as you do, for one can continue the cumulative hierarchy through […]
Comment by Joel David Hamkins on Ackermann's function over the reals
I was trying to convey the idea that there will be many continuous extensions to the reals that obey the Ackermann recursion. Yes, we could pick a specific one, but it seemed more insightful to me to point out that there is some flexibility remaining beyond the recursion, and pointing out exactly where that flexibility […]
Comment by Joel David Hamkins on Ackermann's function over the reals
@alex.peter Don't I address your concern in my sentence asserting, "we must define $A(m,n)$ when $0\leq n\leq 1$ so as to continuously extend what is required when $n=0$ and $n=1$"? It seems we are a little free in those initial boxes in each row. (And I don't understand your concern about linearity, since clearly the […]
Comment by Joel David Hamkins on Inconsistency in a modal logic
Doesn't modality itself allow for this? After all, we can have $\varphi\wedge\psi$ and $\Diamond\neg(\varphi\wedge\psi)$ and $\Diamond\Box(\varphi\wedge\psi)$, which can be seen as ways of asserting that $\varphi$ and $\psi$ are or are not consistent.
Comment by Joel David Hamkins on Large field extensions
There can't be such a field, since it would have to be larger than any given cardinality. (But there could be a class field like this, which contains copies of every set-sized field extension of $k$.)

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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