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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 Nice Algebraic Statements Independent from ZF + V=L (constructibility)
Yes, I believe one can get instances like that from the universal Sigma1 definable sequence.
Comment by Joel David Hamkins on Can the Induction axiom in the Peano arithmetic be replaced by the irrationality of $\sqrt{2}$?
@user6976 My book is available at amazon.com/gp/product/B08942KP4Q.
Comment by Joel David Hamkins on Model theory of the complex numbers with conjugation
Yes, it is a (parametric) bi-interpretation of theories.
Comment by Joel David Hamkins on The easily bored sequence
Nice question! You should say $w$ is nonempty in the claim $R_w(0)\neq R_w(1)$, since this isn't true for the empty word. (Also, you want $v$ nonempty when defining $a$.)
Answer by Joel David Hamkins for Is the one-point compactification of $\mathbb{N}$ computably countable?
The answer is no. Suppose that there are computable functions $q$ and $s$ as you describe. Let $k$ be a program that performs the following task. It starts enumerating $1$s at the start of the sequence until it discovers that $s(k)$ is defined. (We use the Kleene recursion theorem to know that there is such […]
Comment by Joel David Hamkins on Scott's trick without regularity
Sorry, I meant to say $P$ is the class of difference sets, and to refer to the class of ordinals. (But @AsafKaragila, yes, Ord is a set, but in a larger universe!)
Comment by Joel David Hamkins on Scott's trick without regularity
@EmilJeřábek I would encourage you to summarize your comments in an answer. I'm not exactly sure what the question is now.
Comment by Joel David Hamkins on Scott's trick without regularity
Your definition of $P$ seems inside-out. You want $P$ to be the set of difference sets, not the set of ordinals.

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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