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<p>whereas <a href="page.php?w=first-order_logic">first-order</a> and <a href="page.php?w=higher-order_logic">higher-order</a> logic are not. A <a href="page.php?w=Theory_%28mathematical_logic%29">theory</a> (set of sentences <a href="page.php?w=Deductive_closure">closed</a> under <a href="page.php?w=logical_consequence">logical consequence</a>) in a fixed logical system is decidable if there is an effective method for determining whether arbitrary formulas are included in the theory. Many important problems are <a href="page.php?w=undecidable_problem">undecidable</a>,</p><p>
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