L’Innocente, Sonia; Point, Françoise; Toffalori, Carlo On the model theory of the logarithmic function in compact Lie groups. (English) Zbl 1311.03066 J. Algebra Appl. 12, No. 8, Article ID 1350055, 22 p. (2013). Summary: Given a compact linear Lie group \(G\), we form a natural expansion of the theory of the reals where \(G\) and the graph of a logarithm function on \(G\) live. We prove its effective model-completeness and decidability modulo a suitable variant of Schanuel’s Conjecture. MSC: 03C60 Model-theoretic algebra 03C10 Quantifier elimination, model completeness, and related topics 03C64 Model theory of ordered structures; o-minimality 03B25 Decidability of theories and sets of sentences 22E99 Lie groups Keywords:compact Lie groups; effective model completeness; o-minimality; Lang property; Schanuel conjecture PDFBibTeX XMLCite \textit{S. L'Innocente} et al., J. Algebra Appl. 12, No. 8, Article ID 1350055, 22 p. (2013; Zbl 1311.03066) Full Text: DOI References: [1] DOI: 10.1112/jlms/jdn037 · Zbl 1155.03018 · doi:10.1112/jlms/jdn037 [2] DOI: 10.2307/2275634 · Zbl 0899.03026 · doi:10.2307/2275634 [3] DOI: 10.2307/3062133 · Zbl 1026.11038 · doi:10.2307/3062133 [4] DOI: 10.1007/978-94-007-1025-2_5 · doi:10.1007/978-94-007-1025-2_5 [5] Hofmann K. H., Studies in Mathematics 25, in: The Structure of Compact Groups (1998) [6] DOI: 10.1017/CBO9780511810817 · Zbl 0576.15001 · doi:10.1017/CBO9780511810817 [7] DOI: 10.1090/S0894-0347-07-00558-9 · Zbl 1134.03024 · doi:10.1090/S0894-0347-07-00558-9 [8] DOI: 10.1007/BF01388597 · Zbl 0554.10009 · doi:10.1007/BF01388597 [9] DOI: 10.1016/j.apal.2010.06.006 · Zbl 1232.17023 · doi:10.1016/j.apal.2010.06.006 [10] DOI: 10.1017/S0960129508006622 · Zbl 1138.03030 · doi:10.1017/S0960129508006622 [11] A. Macintyre and A. Wilkie, Kreiseliana (A. K. Peters, 1996) pp. 441–467. [12] DOI: 10.2307/27641866 · Zbl 1132.41304 · doi:10.2307/27641866 [13] DOI: 10.1016/0022-4049(88)90125-9 · Zbl 0662.03025 · doi:10.1016/0022-4049(88)90125-9 [14] Price J. F., London Mathematical Society Lecture Note Series 25, in: Lie Groups and Compact Groups (2008) [15] Rossmann W., Lie Groups: An Introduction Through Linear Groups (2002) · Zbl 0989.22001 [16] DOI: 10.1090/S0273-0979-1986-15468-6 · Zbl 0612.03008 · doi:10.1090/S0273-0979-1986-15468-6 [17] DOI: 10.1090/S0894-0347-96-00216-0 · Zbl 0892.03013 · doi:10.1090/S0894-0347-96-00216-0 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.