Joel David Hamkins

mathematics and philosophy of the infinite

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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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Incomparable $omega_1$-like models of set theory | Joel David Hamkins on Every countable model of set theory embeds into its own constructible universe
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Joel David Hamkins on The hierarchy of second-order set theories between GBC and KM and beyond
Neil Barton on The hierarchy of second-order set theories between GBC and KM and beyond

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Comment by Joel David Hamkins on Does ZF+AD settle the original Suslin hypothesis?
Yes, my comment about measurable$\to$tree property$\to$no Suslin trees was too quick, since there are several subtle issues there. Let me reiterate my request for someone to post an answer showing that AD refutes Suslin trees.
Comment by Joel David Hamkins on Does ZF+AD settle the original Suslin hypothesis?
I would be very interested in that, if you can do it.
Comment by Joel David Hamkins on Does ZF+AD settle the original Suslin hypothesis?
Thanks very much for this post! This seems to answer the question I had asked. But in truth, I had had in mind the case where we would also have DC, which I didn't state, and it seems that your technique would not work in that case.
Comment by Joel David Hamkins on Can adding Hilbert's epsilon to a theory, and then expanding that theories axiom schema to include the new language, cause it to become inconsistent?
Yes, but the point is that it makes it confusing to say "the answer is no," as I did in my answer. The answer to the question in the post is no, but the answer to the question in the title is yes.
Does ZF+AD settle the original Suslin hypothesis?
Everyone knows that the real line $\langle\mathbb{R},
Comment by Joel David Hamkins on Can adding Hilbert's epsilon to a theory, and then expanding that theories axiom schema to include the new language, cause it to become inconsistent?
The title question is the opposite of the question asked in the post.
Answer by Joel David Hamkins for Can adding Hilbert's epsilon to a theory, and then expanding that theories axiom schema to include the new language, cause it to become inconsistent?
Even if you're looking at extensions of ZFC, the answer is still no. Consider the theory of ZFC plus the scheme asserting that there is no definable global choice function. That is, the formulas "the class defined by $\varphi(x,y)$ is not a global choice function." This theory is equiconsistent with ZFC, since if we force […]
Comment by Joel David Hamkins on Restricting extenders to a ground model
Does my second example using the rank-to-rank embeddings fulfill your extra property? By combining the (finite iterates of the) embeddings $j_0$ and $j_1$, you build an embedding $j:V_\lambda\to V_\lambda$, which can be extended to $j:V\to M$ with $V_\lambda\subset M$, and $\lambda$ will be the supremum of the critical sequence. If I restrict the embedding to […]

New York Logic

Title TBA
Resource Sharing Linear Logic, I
Sub-Kripkean epistemic models I
Generic logical semantics of justifications III
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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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