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Journal Articles The Journal of Symbolic Logic Year : 2016

The right angle to look at orthogonal sets

Frank Olaf Wagner
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If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable families of commensurable subgroups is shown.


Logic [math.LO]
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Dates and versions

hal-00876033 , version 1 (23-10-2013)
hal-00876033 , version 2 (03-12-2014)
hal-00876033 , version 3 (01-10-2015)
hal-00876033 , version 4 (02-02-2016)
hal-00876033 , version 5 (06-07-2016)


Attribution - NonCommercial - NoDerivatives - CC BY 4.0



Frank Olaf Wagner. The right angle to look at orthogonal sets. The Journal of Symbolic Logic, 2016, 81 (4), pp.1298. ⟨10.1017/jsl.2016.47⟩. ⟨hal-00876033v5⟩
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