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sav08:complete_recursive_axiomatizations [2008/04/06 16:58] vkuncak |
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| ====== Complete Recursive Axiomatizations ====== | ====== Complete Recursive Axiomatizations ====== | ||
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| **Theorem:** Let a set of first-order sentences $Ax$ be a recursively enumerable axiomatization for a [[First-Order Theories|complete and consistent theory]], that is: | **Theorem:** Let a set of first-order sentences $Ax$ be a recursively enumerable axiomatization for a [[First-Order Theories|complete and consistent theory]], that is: | ||
| * $Ax$ is recursively enumerable: there exists an enumerateion $A_1,A_2,\ldots$ of the set $Ax$ and there exists an algorithm that given $i$ computes $A_i$; | * $Ax$ is recursively enumerable: there exists an enumerateion $A_1,A_2,\ldots$ of the set $Ax$ and there exists an algorithm that given $i$ computes $A_i$; | ||