Abstract
Let R be a commutative integral unital domain and L a free noncommutative Lie algebra over R. In this article we show that the ring R and its action on L are 0-interpretable in L, viewed as a ring with the standard ring language. Furthermore, if R has characteristic zero then we prove that the elementary theory of L in the standard ring language is undecidable. To do so we show that the arithmetic is 0-interpretable in L. This implies that the theory of has the independence property. These results answer some old questions on model theory of free Lie algebras.
Original language | English |
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Pages (from-to) | 1204-1216 |
Number of pages | 13 |
Journal | Journal of Symbolic Logic |
Volume | 83 |
Issue number | 3 |
DOIs | |
State | Published - 1 Sep 2018 |
Keywords
- Phraseslie algebra
- elementary theory