Using Non-Standard Techniques to Analyze first-Order Definability over Finite Structures
نویسندگان
چکیده
We present a positive solution to McColm’s conjecture for the special case of decidable theories. This gives a uniform explanation of the separation of fixed-point from first-order definability over a wide range of commonly studied classes of finite structures (including ordered ones). We demonstrate why this result generalizes the standard constructive proofs, and show why it is unlikely that these techniques will ever be able to perform any separation of complexity-theoretic significance!
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