Noah S
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Registered User
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I'm a graduate student at UC Berkeley, studying mathematical logic. I'm especially interested in reverse mathematics and abstract model theory.
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21h |
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What are the main structure theorems on finitely generated commutative monoids? One quick question: you said numerical monoids have not 'been "classified" in any useful sense.' Could you explain what a useful classification would entail? I mean, we know exactly what the numerical monoids are, up to isomorphism. (This is probably a naive question.) |
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21h |
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Hyperbolic sets Fixed spelling |
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1d |
asked | Lawvere’s fixed point theorem and the Recursion Theorem |
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2d |
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Reference request: Minimal Axiomatizations of PA over (+,x,<=). I think the statement of well-ordering should probably be $\exists x(\phi(x))\implies \exists x(\phi(x)\wedge\forall y<x(\neg\phi(x)))$, right? |
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2d |
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A question about large real closed fields If I understand your question correctly, won't the ultrapower of $\kappa^+$-many copies of $\mathbb{R}$ over a regular ultrafilter work? |
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May 17 |
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Is there any proof that you feel you do not “understand”? It seems plausible, but I don't see it immediately. Perhaps I'm being thick: what is the category we live in, in this case? |
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May 17 |
answered | Is there any proof that you feel you do not “understand”? |
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May 16 |
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Are the two meanings of “undecidable” related? (In case it's not clear, history is definitely not my strong point, and I might just be completely wrong here.) |
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May 16 |
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Are the two meanings of “undecidable” related? The "computational system" in Goedel I refer to is the primitive recursive functions. I was under the impression he, already in 1931, thought of them as an important subclass of the (informally) computable functions, and that he was interested in whether there could be a formal definition of "computable;" I may be wrong. As to the "same machinery," I was speaking broadly: both papers develop a coding machinery (Goedel codes proofs, Turing codes machines), and I see the coding machinery as absolutely necessary to the development of each idea; that's all I meant. |
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May 16 |
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Non-standard model of the domination principle Any nonstandard universe will be ill-founded, so not any kind of ordinal at all. "Regularity" can sort of be made sense of, through Bounding schemes; is that in fact what you mean? |
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May 16 |
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Are the two meanings of “undecidable” related? @Joel: I didn't mean "absolute" in the formal sense. My point was just that saying that a proposition is independent of a formal system is clearly relative to that formal system. If we're platonists for a second (which, granted, I tend not to be), then by contrast every set of natural numbers is either computable or incomputable. The only role a theory plays here is telling us which case it is. Two people with different formal systems might disagree on whether a set of natural numbers is computable or not, but they'd still have in mind the same definition of "computable." |
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May 16 |
answered | Basic results with three or more hypotheses |
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May 16 |
revised |
Are the two meanings of “undecidable” related? added 2 characters in body |
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May 16 |
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Are the two meanings of “undecidable” related? So I interpreted "provability" as an instance of the OP's first sense of undecidable, and the second instance being about an individual sentence (and "truth" as neither since Tarski shows that truth is undefinable - I don't think Tarski actually showed that truth was undecidable per se, that requires the coding of computable functions into arithmetic). Maybe I was wrong? |
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May 16 |
answered | Are the two meanings of “undecidable” related? |
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May 16 |
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“Inverse problem” for Brauer groups Ah, I see. Within this question, I'm just interested in the isomorphism types of Brauer groups, not how they interact with each other (although the latter is definitely the "right" way of looking at things in general); I just want to know what groups are Brauer groups of some field. |
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May 16 |
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“Inverse problem” for Brauer groups Hm, I got that value for the Brauer group from pg. 20 of "Lectures on division algebras" by Saltman (books.google.com/…). What is $Br(\mathbb{Q})$? |
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May 16 |
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“Inverse problem” for Brauer groups added 207 characters in body |
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May 16 |
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“Inverse problem” for Brauer groups Thanks! I didn't know that. I've edited appropriately. |
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May 16 |
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“Inverse problem” for Brauer groups edited tags |
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May 16 |
asked | “Inverse problem” for Brauer groups |
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May 7 |
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combinator SSS(SS)SS is not strongly normalizing. Why? Could you give some motivation for this? Why do you suspect it is not strongly normalizing? Also, why is this particular combinator interesting? |
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May 7 |
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Forcing mildly over a worldly cardinal. I don't understand the update - won't $V_{\theta+2}$ and $V_\theta$ agree on whether $V_\theta\models ZFC$? |
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May 7 |
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Forcing mildly over a worldly cardinal. Would you object to the cofinality of $\theta$ being altered? |
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May 1 |
awarded | ● Notable Question |
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May 1 |
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For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? @Omar: strictly speaking, that just proves that no Boolean algebra can come from two different posets. |
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May 1 |
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For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? That may be folklore: it follows from the fact that $\vee$, $\wedge$, and $'$ are all definable from $\le$. |
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May 1 |
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For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? Somewhat tangentially, but I'm curious: for $M$ countably infinite, $\Sigma(M, \times)$ can be thought of as a Borel subset of $2^\omega$, so if uncountable it has cardinality $2^{\aleph_0}$. Is it obvious that $\Sigma'$ behaves similarly? I.e., if $M$ is countable and $\Sigma'(M, \times)$ is uncountable, must $\vert\Sigma'(M, \times\vert=2^{\aleph_0}$? |
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Apr 28 |
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Hahn’s Embedding Theorem and the oldest open question in set theory @Philop: I'm sorry, I misread your response; I've deleted my comments following it. |
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Apr 27 |
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Hahn’s Embedding Theorem and the oldest open question in set theory A possibly related, and probably already answered, question: is "every linearly ordered set is well-ordered" equivalent to AC over ZF? The reason I ask is that it seems plausible for AC, restricted to linearly ordered sets, to be sufficient for Hahn's embedding theorem; and if that were the case, and the answer to the above were "no," then that would show that choice is strictly stronger than Hahn's theorem. |
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Apr 25 |
awarded | ● Nice Answer |
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Apr 24 |
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A Model where Dedekind Reals and Cauchy Reals are Different To clarify, my point isn't even about the strength of the background theory needed (although I am interested in that), but rather (as Colin points out) that a different-"feeling" approach can also give you a separation. (I don't have time right now, but I'll write out the details later today.) |
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Apr 24 |
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A Model where Dedekind Reals and Cauchy Reals are Different @Andrej, I want to apologize for the way I wrote my answer. I just meant that the informal universe your argument takes place in "feels like" a set theory, in a way which similar informal arguments about effectiveness don't, at least to me. I construe "set theory" broadly, here: IZF, ETCS, and ZFC+large cardinals, for example, all fall into this category (I don't know the other theories at all), while RCA doesn't. (Probably "set theory" isn't the right term for it, I'm just not sure what to call that general thing.) Anyways, I've added an explanatory paragraph; I hope this clears things up. |
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Apr 24 |
revised |
A Model where Dedekind Reals and Cauchy Reals are Different added 620 characters in body |
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Apr 24 |
answered | A Model where Dedekind Reals and Cauchy Reals are Different |
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Apr 24 |
awarded | ● Popular Question |
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Apr 24 |
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A Model where Dedekind Reals and Cauchy Reals are Different I think an important point which you need to clarify is what you mean by "model" - in particular, "model of what" and "model in what sense" For instance, I believe there are toposes in which the two notions differ; would you count those as "models"? |
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Apr 18 |
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Ordered groups - examples Taking $m, n=1$ has a natural non-trivial ordering. I think you should sharpen your question. |
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Apr 15 |
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What can the degrees of constructibility be? added 786 characters in body |
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Apr 12 |
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Countable open subgroup Fixed silly mistake |
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Apr 11 |
answered | Countable open subgroup |
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Apr 4 |
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Has the controversy about *fiducial distribution* been settled? What is the controversy in question? |
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Apr 4 |
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Categories of recursive functions @Wouter: If I understand what you're asking, the answer is no: assuming $PA$ is consistent, there are models of $PA$ (hence, satisfying $0\not=1$) which contain internal "proofs" that 0=1. |
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Apr 3 |
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Can the Cantor-Bernstein-Schröder Theorem for proper classes be proven without infinity? What is the axiom of substitution? Is it different from Replacement? |
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Apr 3 |
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Hereditarily Countable Names and Proper Forcing Quick question: normally $\tau\le\sigma$ means $\tau$ is stronger than $\sigma$, but Shelah and a few others use the opposite convention. Which are you using? I presume it's the former, but I just want to check. |
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Apr 2 |
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Godel on recursion-theoretic hierarchies No, I haven't; I'm hesitant to ask for a citation for a claim made in an article now almost 20 years old, but I admit I don't know the etiquette here. Would this be appropriate? |
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Apr 1 |
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Question on da’Costa Logic. Da Costa (en.wikipedia.org/wiki/Newton_da_Costa) has a number of papers, on a variety of logical systems. Could you clarify what you mean by "da Costa's logic?" Or are you asking whether there is any way to formulate naive set theory in paraconsistent logic in an interesting way (to which the answer is surely 'yes')? |
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Mar 31 |
answered | Anick resolution |
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Mar 29 |
asked | Reverse mathematics below RCA |
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Mar 29 |
revised |
Self-containing structures added 158 characters in body |
