## Extensions of Büchi’s problem: questions of decidability for addition and k-th (2005)

Citations: | 3 - 2 self |

### BibTeX

@MISC{Pheidas05extensionsof,

author = {Thanasis Pheidas and Xavier Vidaux},

title = {Extensions of Büchi’s problem: questions of decidability for addition and k-th},

year = {2005}

}

### OpenURL

### Abstract

Abstract. We generalize a question of Büchi: Let R be an integral domain and k ≥ 2 an integer. Is there an algorithm to solve in R any given system of polynomial equations, each of which is linear in the k−th powers of the unknowns? We examine variances of this problem for k = 2, 3 and for R a field of rational functions of characteristic zero. We obtain negative answers, provided that the analogous problem over Z has a negative answer. In particular we prove that the generalization of Büchi’s question for fields of rational functions over a real-closed field F, for k = 2, has a negative answer if the analogous question over Z has a negative answer. 1

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