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 there a physically realizable inductive turing machine that can solve Hilbert's $10$th problem?
Not to mention the further complicating issue that according to some physical theories, the physical universe has finite size, matter and energy.
Comment by Joel David Hamkins on Is there a physically realizable inductive turing machine that can solve Hilbert's $10$th problem?
Computability theory is not really about what is "physically realizable." Are Turing machines themselves physically realizable? No, because once the paper tape becomes large enough, it will have to be in orbit somehow and will inevitably tear; or if it is organized compactly somehow, then it will collapse into a stellar mass or black hole […]
Comment by Joel David Hamkins on Surreal numbers, ultrapowers of $\Bbb R$, ordinal-valued functions and the slow-growing hierarchy
To produce a specific bridgeable class cut in the surreals with no least upper bound, one can successively cut an interval in two, alternately taking the upper or the lower half for the next interval, and at limit stages, taking the interval determined by the surreal filling the set-sized cut determined at that stage and […]
Comment by Joel David Hamkins on Is there a stronger form of recursion?
That's fine about acknowledging me. (Thanks!) About the absorbing ordinals---I haven't absorbed your hyperoperations yet, but if the operations are definable in set theory, then there will always be ordinals that are closed under those operations. One can find them by the replacement axiom: first apply all the operations as much as possible, take a […]
Comment by Joel David Hamkins on Is there a stronger form of recursion?
Can we describe it more simply like this: you consider formal differences $\alpha-\beta$ of ordinals having no common term in their Cantor normal form, and then extend the natural ordinal arithmetic in the natural way (combining/canceling like terms); then take the quotient field; then take the Dedekindian completion (i.e. filling only bridgable gaps, as in […]
Comment by Joel David Hamkins on Is there a stronger form of recursion?
Thanks for the link. I'd suggest dramatically lowering the ratio of background material/new material. You don't need to state the axioms of set theory or develop trivial facts about ordinals. But I do find extremely interesting your proposal to construct the surreals directly from the ordinals. Is there a way for you to summarize this […]
Comment by Joel David Hamkins on Is there a stronger form of recursion?
I would be interested in reading your article when it is available.
Comment by Joel David Hamkins on Notation for "union direct product" of families of sets
I like your proposed notation, and I don't know any standard notation for this. I suppose that another (probably inferior) notation would be $\cup"F_1\times F_2$, since you are taking the image of the product under the binary union function; but I think your proposal is better.

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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Jonsson Dan Saattrup Nielsen

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