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On quotients of the space of orderings of the field ℚ(x)

Paweł GładkiBill Jacob — 2016

Banach Center Publications

In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings ( X ( x ) , G ( x ) ) - it is, in general, nontrivial to determine whether, for a subgroup G G ( x ) the derived quotient structure ( X ( x ) | G , G ) is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

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