The Fraenkel‐Carnap question for Dedekind algebras |
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Authors: | George Weaver Benjamin George |
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Abstract: | It is shown that the second‐order theory of a Dedekind algebra is categorical if it is finitely axiomatizable. This provides a partial answer to an old and neglected question of Fraenkel and Carnap: whether every finitely axiomatizable semantically complete second‐order theory is categorical. It follows that the second‐order theory of a Dedekind algebra is finitely axiomatizable iff the algebra is finitely characterizable. It is also shown that the second‐order theory of a Dedekind algebra is quasi‐finitely axiomatizable iff the algebra is quasi‐finitely characterizable. |
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Keywords: | Second‐order logic categoricity finite axiomatizable |
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