Ashutosh
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Registered User
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May 10 |
revised |
Restrictions of null/meager ideal typos corrected |
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May 10 |
revised |
Restrictions of null/meager ideal added 31 characters in body; added 1 characters in body |
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May 10 |
asked | Restrictions of null/meager ideal |
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May 6 |
revised |
Construction of a maximal ideal added 111 characters in body |
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May 6 |
accepted | Borel ideals on $\omega$ are meager? |
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May 6 |
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Borel ideals on $\omega$ are meager? You are right. No need to extend the ideal. |
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May 6 |
answered | Borel ideals on $\omega$ are meager? |
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May 3 |
accepted | extensions of lebesgue measure |
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May 2 |
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Partition relation, almost a Ramsey cardinal? Define a new coloring $d:[\kappa]^{< \omega} \rightarrow \omega^{< \omega}$ such that for $s \in [\kappa]^{< \omega}$, $d(s)$ encodes the $c$-colors of all finite increasing sequences in $s$. Get an $H \in [\kappa]^{\kappa}$ such that, $(\forall n \in \omega)|d([H]^n)| \leq 16$. Let $s_1^{0}, s_1^{1}, s_2^{0}, s_2^1, \dots , s_5^0, s_5^1 \in [H]^m$ be a sequence of sets such that max of each set is less than the min of next one and $c(s_i^0) \neq c(s_i^1)$, for $1 \leq i \leq 5$. But this meanss $|d([H]^{5m}| \geq 32$. |
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May 2 |
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Partition relation, almost a Ramsey cardinal? Suppose (for example), that for every coloring $c:[\kappa]^{< \omega} \rightarrow \omega$, there is a set $H \in [\kappa]^\kappa$ such that $(\forall n \in \omega)|c([H]^n)| \leq 16$. Note that this implies that cofinality of $\kappa$ is at least $\omega_1$. Let us try to bring $16$ down to $1$. Assume that this is impossible for some coloring $c$. Then for every $\kappa$ sized subset $A \subseteq \kappa$, there is some $m$ and there are arbitrarily long sequences $s_1, s_2, \dots s_k \in [A]^{m}$ such that max$(s_i) <$ min$(s_{i+1})$ and $c(s_i) \neq c(s_{i+1})$. |
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Apr 29 |
answered | extensions of lebesgue measure |
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Feb 17 |
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totally ordered chain in the powerset with big cardinality Here's a reference: William Mitchell - Aronszajn trees and the independence of the transfer property, Annals of Math. Logic., Vol. 5, Issue 1, 1972, pp. 21-46 |
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Feb 17 |
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totally ordered chain in the powerset with big cardinality If I remember correctly, William Mitchell has shown in his thesis that if you add $\omega_{\omega_1}$ Cohen reals to the universe then in the resulting model there is no subset of $\mathcal{P}(\omega_1)$ of size $2^{\omega_1}$ which is linearly ordered under inclusion. |
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Feb 12 |
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A question about definable non-empty sets containing no definable elements. One can avoid inaccessibles by appealing to Shelah's model where a similar result holds for sets with Baire property. |
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Feb 12 |
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A question about definable non-empty sets containing no definable elements. Doesn't Solovay's model of ZFC + "All HOD(R) sets of reals are Lebesgue measurable" witness that, for any definable set (without parameters), ZFC cannot prove that such a set is Lebesgue non measurable? |
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Jan 31 |
awarded | ● Enthusiast |
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Jan 20 |
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Even XOR Odd Infinities? If $x + x = 0$ and $y + y = 1$, then $x = x(y + y) = xy + xy = (x + x)y = 0$. |
