Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2034

Preprint Number 2034

Previous Next Preprint server

2034. M. Malliaris and S. Shelah
New simple theories from hypergraph sequences

Submission date: 12 August 2021


We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not require familiarity with the earlier proof.) We prove a model-completion and quantifier-elimination result for theories in this family. We develop a combinatorial property which they share. We invoke regular ultrafilters to show the strength of this property, showing that any flexible ultrafilter which is good for the random graph is able to saturate such theories.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2108.05526: pdf, ps.

Last updated: August 23 2021 16:55 Please send your corrections to: