Interpreting a field in its Heisenberg group
Interpreting a field in its Heisenberg group
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解释海森堡群中的域
DOI：
10.1017/jsl.2021.107
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Weisshaar, R.
中科院分区：
文献类型：
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作者：
Alvir, R.;Calvert, W.;Goodman, G.;Harizanov, V.;Knight, J.;Morozov, A.;Miller, R.;Soskova, A.;Weisshaar, R.
改进和推广了Maltsev在1960年的一个结果.对于域F，我们用元素在F中的海森堡群来表示。Maltsev表明，有一个副本的F定义，使用存在公式与任意非交换对元素作为参数。我们表明，F的解释使用可计算的公式，没有参数。我们给出两个证明。第一个是存在性证明，依赖于Harrison-Trainor，Melnikov，R。米勒和蒙塔尔班。这个证明允许的可能性，F的元素表示的元组中没有固定的arity。第二个证明是直接的，给出定义解释的显式有限存在公式，F的元素由中的三元组表示。看看什么是用来达到这个参数免费的F的解释，我们给出了一般条件足以消除参数的解释。
We improve on and generalize a 1960 result of Maltsev. For a field F, we denote by the Heisenberg group with entries in F. Maltsev showed that there is a copy of F defined in , using existential formulas with an arbitrary non-commuting pair of elements as parameters. We show that F is interpreted in using computable formulas with no parameters. We give two proofs. The first is an existence proof, relying on a result of Harrison-Trainor, Melnikov, R. Miller, and Montalbán. This proof allows the possibility that the elements of F are represented by tuples in of no fixed arity. The second proof is direct, giving explicit finitary existential formulas that define the interpretation, with elements of F represented by triples in . Looking at what was used to arrive at this parameter-free interpretation of F in , we give general conditions sufficient to eliminate parameters from interpretations.