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 Yearling
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  • 0 posts edited
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  • 27 votes cast
Oct
14
comment Why is the intersection of countably many homogeneously Suslin subsets of $\,^{\omega} \omega$ homogeneously Suslin?
You are right, that doesn't seem to be the same. I don't know if the proof would be different. Still, in "The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal", Lemma 2.11. on p. 27, the statement appears for homogeneously Suslin sets.
Oct
12
comment Show that $\{ a_n \}$ converges.
Prove that $a_n$ is increasing. This can be done by using $a_n < 2$, which you already proved.
Oct
11
revised Why is the intersection of countably many homogeneously Suslin subsets of $\,^{\omega} \omega$ homogeneously Suslin?
added 95 characters in body
Oct
11
revised Why is the intersection of countably many homogeneously Suslin subsets of $\,^{\omega} \omega$ homogeneously Suslin?
edited tags
Oct
11
revised Why is the intersection of countably many homogeneously Suslin subsets of $\,^{\omega} \omega$ homogeneously Suslin?
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Oct
11
revised Why is the intersection of countably many homogeneously Suslin subsets of $\,^{\omega} \omega$ homogeneously Suslin?
added 541 characters in body
Oct
11
asked Why is the intersection of countably many homogeneously Suslin subsets of $\,^{\omega} \omega$ homogeneously Suslin?
Oct
2
comment There are 4 girls and 3 boys but only 5 seats. How many ways to seat the 3 boys together?
Seems correct to me.
Sep
20
accepted Are there meaningful elementary embeddings of transitive models of set theory without a critical point?
Sep
18
answered Are there meaningful elementary embeddings of transitive models of set theory without a critical point?
Sep
18
revised Are there meaningful elementary embeddings of transitive models of set theory without a critical point?
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Sep
18
comment Are there meaningful elementary embeddings of transitive models of set theory without a critical point?
Oh, Sorry, I meant that $j$ does not map every element of $M$ to itself, i.e. is not inclusion, but I wrote $j\neq id$. I'm going to change it.
Sep
18
asked Are there meaningful elementary embeddings of transitive models of set theory without a critical point?
Sep
17
awarded  Yearling
Sep
15
comment 1. Measurable sets : uncountable union, 2. null set is disjoint from translated rationals
Um, I can't see anything wrong with my post as it is now though.
Sep
15
comment 1. Measurable sets : uncountable union, 2. null set is disjoint from translated rationals
Note that I was talking about the set $\textbf{remaining}$ after subtracting the obviously open part, as in Both Htob's approach.
Sep
15
comment 1. Measurable sets : uncountable union, 2. null set is disjoint from translated rationals
We have $A+1 = \{ x+1 \, |\, x\in A\} = \bigcup_{x\in A} \{x+1\}$ and $A-1 = \{ x-1 \, |\, x\in A\} = \bigcup_{x\in A} \{ x-1\}$. These are the definitions of the translations of $A$ by $1$ and $-1$ respectively. Then clearly $\bigcup_{x\in A} \{x+1,x-1\} = \bigcup_{x\in A} \{x+1\} \cup \bigcup_{x\in A} \{x-1\} = (A+1) \cup (A-1)$.
Sep
15
comment Sum from $i$ to $\lg(n)$
Well if $m = 2^n$, then by definition of the logarithm $n = log_2(m)$. So if $t_{2^n}$ can be decribed with some formula depending with variable $n$, $t_{2^n} = f(n)$, then $t_m = f(log_2(m))$. So I replaced every instance of $n$ in the formula $f(n)$ by $log_2(n)$ and simplified.
Sep
14
comment Intersection of Borel subset with line
Yes, that's it.
Sep
13
comment Intersection of Borel subset with line
The statement in that link is a different one. If $A\subseteq \mathbb{R}^2$ is Borel, then it is not in general true that $\{ x\in \mathbb{R} \, |\, \exists y\in \mathbb{R} (x,y)\in A\}$ is Borel. The proof is not (very) simple. But it is true that for any specific $y\in \mathbb{R}$ the set $\{ x\in \mathbb{R} \, |\, (x,y)\in A\}$ is Borel. Do you see the difference?