Submission date: 17 June 2017

Abstract:

We introduce a notion weaker than half of a bi-interpretation which we call a semi-retraction (after [ahzi86]). We say a countable structure is Ramsey if its age is a Ramsey class (as defined in [ne05]). For a countable Ramsey structure B we show a countable semi-retraction A of B must also be Ramsey. We also introduce notation for what we call semi-direct product structures, after the group construction known to preserve the Ramsey property. [kpt05] We use a weakening of semi-retraction to give a finitary argument for why semi-direct product structures of Ramsey structures must be Ramsey.

Mathematics Subject Classification: 05C55, 03C30, 03C45

Keywords and phrases:

Full text arXiv 1706.05558: pdf, ps.