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Preprint Number 937

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937. Zaniar Ghadernezhad
The small index property of automorphism groups of ab-initio generic structures
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Submission date: 2 October 2015.

Abstract:

Suppose M is a countable ab-initio (uncollapsed) generic structure which is obtained from a pre-dimension function with rational coefficients. We show that if H is a subgroup of Aut(M) with [Aut(M):H]<2^{ℵ_0}, then there exists a finite set A ⊆ M such that Aut_A(M) ⊆ H.

This shows that Aut(M) has the small index property.

Mathematics Subject Classification: 03C15, 20B07, 20B27

Keywords and phrases:

Full text arXiv 1510.00586: pdf, ps.


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