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bio website comp.nus.edu.sg/~a0078129
location Singapore
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Problem mining.


Feb
15
accepted Consequences of ZF+“all subsets of reals are Lebesgue measurable”
Feb
4
answered What are your favorite instructional counterexamples?
Jan
22
comment Consequences of ZF+“all subsets of reals are Lebesgue measurable”
@AndresCaicedo: I did have in mind that the length of an interval equals its measure.
Jan
22
comment Consequences of ZF+“all subsets of reals are Lebesgue measurable”
@Burak: I mean ~CH is a consequence of ZFC + there is a measure on \mathbb{R}, and this measure is necessarily not Lebesgue. You are right over ZF they are not really orthogonal.
Jan
22
revised Consequences of ZF+“all subsets of reals are Lebesgue measurable”
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Jan
22
comment Consequences of ZF+“all subsets of reals are Lebesgue measurable”
I meant Lebesgue measure is total otherwise choice is not necessarily ruled out. Sorry for the ambiguity.
Jan
22
revised Consequences of ZF+“all subsets of reals are Lebesgue measurable”
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Jan
22
revised Consequences of ZF+“all subsets of reals are Lebesgue measurable”
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Jan
22
comment Consequences of ZF+“all subsets of reals are Lebesgue measurable”
Sorry Cantor space and R confusion. I remedied this. Isn't that such measure simply does not exist if R is a countable union of countable sets, by $\sigma$-additivity?
Jan
22
revised Consequences of ZF+“all subsets of reals are Lebesgue measurable”
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Jan
22
comment Consequences of ZF+“all subsets of reals are Lebesgue measurable”
@AndresCaicedo: thanks! Which survey by Fremlin do you refer to?
Jan
22
revised Consequences of ZF+“all subsets of reals are Lebesgue measurable”
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Jan
22
comment Consequences of ZF+“all subsets of reals are Lebesgue measurable”
@bof,@Jesse: the negation of CH is indeed a consequence of ZFC+exists a total measure. What I'm really interested is the extension of Lebesgue measure. I'll edit the question.
Jan
22
revised Consequences of ZF+“all subsets of reals are Lebesgue measurable”
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Jan
22
asked Consequences of ZF+“all subsets of reals are Lebesgue measurable”
Jan
13
comment Does PA prove a sentence asserting that all of I-sigma(n) theories are consistent?
Suppose you could formalize $\forall n I\Sigma_n^0$ in PA in the first place, then for any model of PA, $\{n: I\Sigma_n^0\vdash \varphi\}$ is an arithmetic set in the model. Take the least element and it would be a real natural number.
Jan
11
answered Does PA prove a sentence asserting that all of I-sigma(n) theories are consistent?
Nov
10
comment Cohesive set with degree below non-high Martin-Löf random reals
So the question is really for MLR which neither low or high.
Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious