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On the model theory of the logarithmic function in compact Lie groups. (English) Zbl 1311.03066

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
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