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Preprint Number 1542

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1542. Tomasz Rzepecki
Hereditary G-compactness

Submission date: 19 December 2018


We introduce the notion of hereditary G-compactness (with respect to interpretation). We provide a sufficient condition for a poset to not be hereditarily G-compact, which we use to show that any linear order is not hereditarily G-compact. Assuming that a long-standing conjecture about unstable NIP theories holds, this implies that an NIP theory is hereditarily G-compact if and only if it is stable. We show that if G is definable over A in a hereditarily G-compact theory, then G^{00}_A=G^{000}_A.

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Full text arXiv 1812.08081: pdf, ps.

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