Tarski, A., Mostowski, A., Robinson, R. M. (1953). Undecidability and essential undecidability in arithmetic.  Home/Search   Document Not in Database   Summary   Related Articles

....have to make sure that a certain relation on the universe is Noetherian. This is an inherent property of the model, since the well foundedness of a relation is not expressible in first order logic. Several other methods for proving undecidability of theories have been proposed in the literature. Tarski (1953) shows that a theory T is undecidable if some essentially undecidable and finitely axiomatizable theory T 0 (for instance the theory Q (Tarski et al. 1953a) is relatively weakly interpretable in T . In order to show relative weak interpretability of T 0 in T one has to find first order ....

....relation is not expressible in first order logic. Several other methods for proving undecidability of theories have been proposed in the literature. Tarski (1953) shows that a theory T is undecidable if some essentially undecidable and finitely axiomatizable theory T 0 (for instance the theory Q (Tarski et al. 1953a) is relatively weakly interpretable in T . In order to show relative weak interpretability of T 0 in T one has to find first order formulas defining the universe and operations of T 0 in some consistent extension of T . Hence the correspondence between the theories is expressed completely ....

Tarski, A., Mostowski, A., Robinson, R. M. (1953). Undecidability and essential undecidability in arithmetic.

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