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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 Question about a family of nested countable subsets of $\mathbb{R}$
@EmilJeřábek why not post an answer explicating the argument of your comment?
Comment by Joel David Hamkins on Is this cardinal characteristic trivial? (Number of strategies needed to guarantee at least one win)
The diagonalization argument Patrick presumably alludes to shows that $\text{cof}(2^{\aleph_0})\leq\mathfrak{g}$. Namely, enumerate all the strategies, and then create a game such that for every bounded collection of the strategies in the enumeration, there is a constant-play strategy defeating those strategies.
Comment by Joel David Hamkins on Wild classification problems and Borel reducibility
@BenjaminSteinberg Borel complexity subsumes arithmetic complexity and far more---it is Delta^1_1---and so there aren't generally results along the lines you suggest. This is a step up from computability. Practitioners identify the Borel realm with "explicit" mathematics.
Comment by Joel David Hamkins on First use of corner quotes for Gödel numbers
I voted to reopen, since I find the question interesting on this site. (The fact that a question would also fit on another site is not a reason to close on any one of them, since many questions fit on several sites.)
Comment by Joel David Hamkins on What is the canonical way to extend Peano's axioms to the set of all integers?
Some people refer to Dedekind arithmetic as "Peano arithmetic" or as "second-order Peano arithmetic", in light of Peano's brilliant presentation of the theory, but Peano himself credits Dedekind.
Comment by Joel David Hamkins on What is the canonical way to extend Peano's axioms to the set of all integers?
I think there is some confusion in the comments and the question between Peano arithmetic and Dedekind arithmetic. Dedekind defined his (second-order) arithmetic in the signature with only 0 and successor S, and then proves that + and * are second-order definable by a recursive definition. What is called Peano arithmetic PA, in contrast, is […]
Answer by Joel David Hamkins for What is the canonical way to extend Peano's axioms to the set of all integers?
Here is a somewhat different way to think about it, although the result is equivalent to the theories in the other answers. Begin with the observation that the structures $\langle\mathbb{N},+,\cdot,0,1,
Comment by Joel David Hamkins on What is the shape of large cardinal tree in implication strength order?
@JosephVanName That is extremely interesting. Let's discuss this further by email.

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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