Submission date: 28 February 2017

Abstract:

A relational first order structure M is elementarily indivisible if for every coloring of its universe in two colors, there is a monochromatic elementary substructure which is isomorphic to M. In this paper, we generalize the lexicographic product of relational first order structures, as defined in a previous paper by the author, and construct a product of infinitely many relational structures. We prove that this product, in some sense, preservers the notion of ultrahomogeneity and use this result to construct a rigid elementarily indivisible structure, answering the last open question from a paper by A. Hasson, M. Kojman and A. Onshuus.

Mathematics Subject Classification: 03C10, 03C20, 03C75, 05D10, 05C55

Keywords and phrases:

Full text arXiv 1702.08766: pdf, ps.