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- W2950660147 abstract "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. We consider computability of this set for subrings R of the rationals. Applying Baire category theory to these subrings, which naturally form a topological space, relates their sets HTP(R) to the set HTP($mathbb{Q}$), whose decidability remains an open question. The main result is that, for an arbitrary set C, HTP($mathbb{Q}$) computes C if and only if the subrings R for which HTP(R) computes C form a nonmeager class. Similar results hold for 1-reducibility, for admitting a Diophantine model of $mathbb{Z}$, and for existential definability of $mathbb{Z}$." @default.
- W2950660147 created "2019-06-27" @default.
- W2950660147 creator A5056097245 @default.
- W2950660147 date "2016-02-10" @default.
- W2950660147 modified "2023-09-30" @default.
- W2950660147 title "Baire category theory and Hilbert's Tenth Problem inside $mathbb{Q}$" @default.
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