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Ali Enayat

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Name Ali Enayat
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Seen May 21 at 21:32
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May
11
 accepted How long can it take to generate a $\sigma$-algebra?
May
9
 comment How long can it take to generate a $\sigma$-algebra?
Thank you François for fixing the link.
May
9
 comment How long can it take to generate a $\sigma$-algebra?
@François: there is only issue of clarity, not veracity; the current edit addresses that.
May
9
 revised How long can it take to generate a $\sigma$-algebra?
added 394 characters in body
May
8
 comment How long can it take to generate a $\sigma$-algebra?
@Tomek: thanks, you are right. I will edit my answer.
May
8
 answered How long can it take to generate a $\sigma$-algebra?
Apr
13
 accepted A Fraïssé class without the strong amalgamation property.
Apr
12
 revised A Fraïssé class without the strong amalgamation property.
added 67 characters in body
Apr
12
 comment When does $ZFC \vdash\ ‘ ZFC \vdash \varphi\ ’$ imply $ZFC \vdash \varphi$?
In the last line, "$\omega$-standard" was meant to be "$\omega$-nonstandard", I fixed that.
Apr
12
 revised When does $ZFC \vdash\ ‘ ZFC \vdash \varphi\ ’$ imply $ZFC \vdash \varphi$?
Changed $\omega$-standard to $\omega$-nonstandard in the last line.
Apr
12
 revised A Fraïssé class without the strong amalgamation property.
added 553 characters in body
Apr
12
 revised A Fraïssé class without the strong amalgamation property.
deleted 182 characters in body
Apr
12
 revised A Fraïssé class without the strong amalgamation property.
added 11 characters in body
Apr
12
 comment A Fraïssé class without the strong amalgamation property.
@Joel: the theorem was (implicitly) stated for relational structures, and your proposed fix is the right one when there are function symbols around. I will edit.
Apr
11
 answered A Fraïssé class without the strong amalgamation property.
Apr
9
 comment dense orders are saturated
@Philip: in the second emendation; Vladmir's name has morphed to Victor.
Apr
9
 comment dense orders are saturated
My guess is that after the appearance of the paper of Erdős at al., the result you are interested in became "common knowledge" among the cognoscenti; which is corroborated by the fact that, similar to many venerable theorems, it was "demoted" to an exercise in Marker's text.
Apr
9
 comment dense orders are saturated
@Vladimir: you are right that the statement of Theorem 2.1 of the paper by Erdős et al. does not yield the result you are interested in. However, the proof of Theorem 2.1 is carried out by a back-and-forth argument, a key step of which involves the key idea of reducing the realizability of a type in the language of ordered fields, to a purely order-theoretic type, which is precisely what is needed to prove the result you are interested in (note that this proof does not invoke Tarski's elimination of quantifiers in real closed fields)--(continued in the next comment).
Apr
9
 comment ERA, PRA, PA, transfinite induction and equivalences
Emil: thanks for your detailed explanations (I only now saw them).
Apr
8
 revised dense orders are saturated
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Apr
8
 comment dense orders are saturated
Philip, thanks for the historical tidbits in your emendation; I was not aware of the work of Hausdorff, nor of the connection between the work of Alling and that of Erdös et al. It is amusing that Alling's paper came out in the same year as the classical paper of Morley and Vaught on saturated models (Homogeneous universal models. Math. Scand. 11 1962, 37–57).
Apr
8
 answered dense orders are saturated
Mar
29
 comment Reverse mathematics below RCA
@Noah, have you seen the very last section of Simpson's book on Subsystems of Second Order Arithmetic? It might be of interest.
Mar
29
 comment More on Kunen’s inconsistency result
Nice answer Joel. By the way, the well-foundedness of the direct limit should also be addressed.
Mar
24
 answered Self-containing structures
Mar
20
 comment Consistency of many Erdos cardinals
Since every (uncountable) measurable cardinal is an Erdős cardinal, a safe upper bound to "$\kappa(\alpha)$ exists for each $\alpha$ is "the measurable cardinals are cofinal in the ordinals". Jech's text, as well as Kanamori's has the full details. Are you looking for sharper upper bounds?
Mar
16
 comment Similarities between Post’s Problem and Cohen’s Forcing
@ Noah: thanks for adding the link.
Mar
15
 accepted Bijective-equivalent collections of proper classes in set theory
Mar
15
 comment What follows from assuming not Con(ZF)?
I suggest looking at the answers to the following related question (in the context of $PA$). mathoverflow.net/questions/65837/…
Mar
15
 revised Bijective-equivalent collections of proper classes in set theory
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Mar
15
 answered Bijective-equivalent collections of proper classes in set theory
Mar
11
 revised Similarities between Post’s Problem and Cohen’s Forcing
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Mar
10
 revised How long should one wait for a report before asking about its status?
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Mar
10
 comment How long should one wait for a report before asking about its status?
@quid: I did not mean to write an algorithm, but rather, general advice. But since you asked: "within a week" is a good approximation to "shortly thereafter".
Mar
10
 comment How long should one wait for a report before asking about its status?
@quid: it is one thing for the journal to acknowledge receipt, and a whole other thing, based on the two factors I enumerated, for the editor to have a reliable time-estimate (hence the "shortly after").
Mar
10
 answered How long should one wait for a report before asking about its status?
Mar
9
 awarded ● Nice Answer
Mar
8
 answered Similarities between Post’s Problem and Cohen’s Forcing
Mar
7
 revised Topological characterization of the closed interval $[0,1]$.
added 45 characters in body
Mar
7
 awarded ● Nice Answer
Mar
7
 comment Topological characterization of the closed interval $[0,1]$.
@Martin: the edit was prompted by your remark and that of Ramiro.
Mar
7
 comment Topological characterization of the closed interval $[0,1]$.
@Ramiro: thanks for the pointer; I noticed another way to couch the result in terms of purely topological notions (as in the edit).
Mar
7
 revised Topological characterization of the closed interval $[0,1]$.
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Mar
7
 comment Topological characterization of the closed interval $[0,1]$.
@Martin: admittedly this is not a purely topological characterization, but clearly topology plays a pivotal role in its formulation (continuity of $f$ with respect to the product topology on $X^2$ induced by the order topology on $X$).
Mar
6
 comment Reflection principles
I am with Andreas in his interpretation; and I suspect that the phrase "is satisfied" at the end of the question was meant to be "is satisfied in M$. In this reading, the answer is clearly YES.
Mar
6
 revised Topological characterization of the closed interval $[0,1]$.
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Mar
6
 comment ERA, PRA, PA, transfinite induction and equivalences
Emil: can you recommend some references for the results in #2 in connection with fragments of arithmetic?
Mar
6
 answered Topological characterization of the closed interval $[0,1]$.
Mar
1
 comment A linear order obtained by forcing with P(omega)/fin
Paul, I am curious to know whether your line of reasoning can be used to answer the following somewhat related MO question that has remained unsolved: mathoverflow.net/questions/24047/…
Feb
28
 answered Are all models of ZF + DC + “All set of reals are lebesgue measurable” also models of CH?