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<a accesskey="3" href="page.php?w=consistency&amp;p=2">3.Next</a>
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<p>In <a href="page.php?w=deductive_logic">deductive logic</a>, a <b>consistent</b> <a href="page.php?w=theory_%28mathematical_logic%29">theory</a> is one that does not lead to a logical <a href="page.php?w=contradiction">contradiction</a>. A theory  is consistent if there is no <a href="page.php?w=Formula_%28mathematical_logic%29">formula</a>  such that both  and its negation  are elements of the set of consequences of . Let  be a set of <a href="page.php?w=Closed-form_expression">closed sentences</a> (informally "axioms") and  the set of closed</p><p>
<a accesskey="3" href="page.php?w=consistency&amp;p=2">3.Next</a>
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