<?xml version="1.0" encoding='utf-8'?>
<!DOCTYPE wml PUBLIC "-//WAPFORUM//DTD WML 1.1//EN" "http://www.wapforum.org/DTD/wml_1.1.xml">
<wml>
<card id="card1" title="Hardy hierarchy - Page 2 - Wikipedia">
<p>
<a accesskey="1" href="page.php?w=Hardy_hierarchy&amp;p=1">1.Previous</a><br />
<a accesskey="3" href="page.php?w=Hardy_hierarchy&amp;p=3">3.Next</a>
</p>
<p>called <b>Hardy functions</b>. It is related to the <a href="page.php?w=fast-growing_hierarchy">fast-growing hierarchy</a> and <a href="page.php?w=slow-growing_hierarchy">slow-growing hierarchy</a>.</p>

<p>The Hardy hierarchy was introduced by Stanley S. Wainer in 1972, but the idea of its definition comes from Hardy's 1904 paper, in which Hardy exhibits a set of reals with cardinality .</p>

<p><big> Definition </big></p>
<p>Let u be a <a href="page.php?w=large_countable_ordinal">large countable ordinal</a> such that a <a href="page.php?w=fundamental_sequence_%28ordinals%29">fundamental sequence</a></p><p>
<a accesskey="1" href="page.php?w=Hardy_hierarchy&amp;p=1">1.Previous</a><br />
<a accesskey="3" href="page.php?w=Hardy_hierarchy&amp;p=3">3.Next</a>
</p>

<do type="prev" label="Search">
        <go href="search.wml"/>
</do>

</card>
</wml>
