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<p>and over <a href="page.php?w=intuitionistic_logic">intuitionistic logic</a>.</p>

<p><big>Cantor's theorem</big></p>
<p>Another difficulty with the idea of a universal set concerns the <a href="page.php?w=power_set">power set</a> of the set of all sets. Because this power set is a set of sets, it would necessarily be a subset of the set of all sets, provided that both exist.  However, this conflicts with Cantor's theorem that the power set of any set (whether infinite or not) always has strictly higher <a href="page.php?w=cardinality">cardinality</a> than</p><p>
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