Von Neumann coordinatization is not first-order
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2004-09-15 | |
| dc.date | 2006-01-28 | |
| dc.date.accessioned | 2026-07-07T06:38:48Z | |
| dc.date.available | 2026-07-07T06:38:48Z | |
| dc.description | A lattice L is coordinatizable, if it is isomorphic to the lattice L(R) of principal right ideals of some von Neumann regular ring R. This forces L to be complemented modular. All known sufficient conditions for coordinatizability, due first to J. von Neumann, then to B. Jonsson, are first-order. Nevertheless, we prove that coordinatizability of lattices is not first-order, by finding a non-coordinatizable lattice K with a coordinatizable countable elementary extension L. This solves a 1960 problem of B. Jonsson. We also prove that there is no L\_{infinity, infinity} statement equivalent to coordinatizability. Furthermore, the class of coordinatizable lattices is not closed under countable directed unions; this solves another problem of B. Jonsson from 1962. | |
| dc.identifier | https://arxiv.org/abs/math/0409250 | |
| dc.identifier | http://arxiv.org/abs/math/0409250 | |
| dc.identifier | Journal of Mathematical Logic 6, no. 1 (2006) 1--24 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100866 | |
| dc.subject | General Mathematics | |
| dc.subject | General Topology | |
| dc.subject | Logic | |
| dc.subject | Rings and Algebras | |
| dc.subject | AMS: 06C20, 06C05, 06B20, 03C10, 03C90, 16E50 | |
| dc.title | Von Neumann coordinatization is not first-order | |
| dc.type | text |