# MEASURE THEORY AND HILBERT’S TENTH PROBLEM INSIDE ℚ

```@inproceedings{Miller2017MEASURETA,
title={MEASURE THEORY AND HILBERT’S TENTH PROBLEM INSIDE ℚ},
author={Russell G. Miller},
year={2017}
}```
For a ring R, Hilbert’s Tenth Problem HTP(R) is the set of polynomial equations over R, in several variables, with solutions in R. When R = Z, it is known that the jump Z′ is Turing-reducible to HTP(Z). We consider computability of HTP(R) for subrings R of the rationals. Applying measure theory to these subrings, which naturally form a measure space, relates their sets HTP(R) to the set HTP(Q), whose decidability remains an open question. We raise the question of the measure of the topological…
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