The Woods–Erdös conjecture for polynomial rings

Annals of Pure and Applied Logic 113 (1-3):331-344 (2001)
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Abstract

The elementary theories of polynomial rings over finite fields with the coprimeness predicate and two kinds of “successor” functions are studied. It is proved that equality is definable in these languages. This gives an affirmative answer to the polynomial analogue of the Woods–Erdös conjecture. It is also proved that these theories are undecidable

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10.1016/s0168-0072(01)00065-3

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Definability and decision problems in arithmetic.Julia Robinson - 1949 - Journal of Symbolic Logic 14 (2):98-114.

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