most recent 30 from http://mathoverflow.net 2013-05-18T17:29:18Z http://mathoverflow.net/feeds/user/11304 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48246/recursive-non-well-orders-that-are-sneaky-but-not-that-sneaky anonymous 2010-12-04T04:31:02Z 2010-12-04T04:31:02Z

<p>This is a variant on <a href="http://mathoverflow.net/questions/30633/sneaky-recursive-non-well-orders" rel="nofollow">http://mathoverflow.net/questions/30633/sneaky-recursive-non-well-orders</a> where it was asked</p> <blockquote> <p>Is there a recursive function $f$ such that whenever $a\in\mathcal{O}$, $f(a)$ is a Turing index for a linear non-well-order with no $H_a$ -computable descending chain?</p> </blockquote> <p>The answer to the original question gave a single non-well-order with no hyperarithmetic descending chain at all. Instead can $f(a)$ be a non-well-order with an $H_a$-computable descending chain but no $H_b$-computable descending chain for $b &lt;_{\mathcal{O}} a$ ? </p>