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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 Can passing to a larger Grothendieck universe ever lead to category-theoretic complications?
This paper is all about the situation described in the beginning of the question: [2009.07164] Categorical large cardinals and the tension between categoricity and set-theoretic reflection arxiv.org/abs/2009.07164.
Comment by Joel David Hamkins on Transcendence degree of the surreals over the subfield generated by the ordinals
I would appreciate fuller explanation of this answer, if it would be possible.
Comment by Joel David Hamkins on Are there substantive differences between the different approaches to "size issues" in category theory?
@JoeLamond You say it is reflexive if $\kappa$ is small, but the link you provided said it is reflexive only if $\kappa$ is small. Those are not the same, so I am not sure what the true state is. But also, neither of those statements state whether there is a universal claim to be made. […]
Comment by Joel David Hamkins on Forcing with strong binary trees
Can one implement the fusion arguments? It seems delicate to enforce the strong splitting requirement...
Comment by Joel David Hamkins on Interpretability and relative consistency with Kolmogorov randomness axioms
Can you tell us what is $R$?
Comment by Joel David Hamkins on What tools are there, apart from using the countable chain condition, to show that forcing preserves cardinals?
Perhaps someone should collect the various ideas in the comments and post an answer? I think the site works better when answers are posted as answers.
Comment by Joel David Hamkins on What tools are there, apart from using the countable chain condition, to show that forcing preserves cardinals?
In case you are not aware, the generalized Delta-system lemma (theorem 9.19 in Jech) is extremely useful for proving instances of $\delta$-c.c. for higher cardinals, including your case. Also, an often useful variation of closure would be strategic closure, which shows that no new sequences of a certain length over the ground model are added, […]
Comment by Joel David Hamkins on Full name (in the sense of forcing) for a partial order
This is also possible, since we can mix the names $\tau$ that I had used, with condition $p$, with the name $1_\pi$ having value $\neg p$. That was my first idea, actually, but I realized this complication was not needed for the version of fullness you had stated.

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