The space of minimal structures
| dc.contributor.author | Belegradek, Oleg V. | |
| dc.date.accessioned | 2021-06-16T07:39:33Z | |
| dc.date.available | 2021-06-16T07:39:33Z | |
| dc.date.issued | 2014-02 | |
| dc.description.abstract | For a signature L with at least one constant symbol, an L-structure is called minimal if it has no proper substructures. Let SL be the set of isomorphism types of minimal L-structures. The elements of SL can be identified with ultrafilters of the Boolean algebra of quantifier-free L-sentences, and therefore one can define a Stone topology on SL. This topology on SL generalizes the topology of the space of n-marked groups. We introduce a natural ultrametric on SL, and show that the Stone topology on SL coincides with the topology of the ultrametric space SL iff the ultrametric space SL is compact iff L is locally finite (that is, L contains finitely many n-ary symbols for any n<?). As one of the applications of compactness of the Stone topology on SL, we prove compactness of certain classes of metric spaces in the Gromov-Hausdorff topology. This slightly refines the known result based on Gromov's ideas that any uniformly totally bounded class of compact metric spaces is precompact. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. | en_US |
| dc.fullTextLevel | Full Text | en_US |
| dc.identifier.doi | 10.1002/malq.201300012 | en_US |
| dc.identifier.issn | 1521-3870 | |
| dc.identifier.scopus | 2-s2.0-84893655541 | en_US |
| dc.identifier.uri | https://hdl.handle.net/11411/3772 | |
| dc.identifier.uri | https://doi.org/10.1002/malq.201300012 | |
| dc.identifier.wos | WOS:000331901500006 | en_US |
| dc.identifier.wosquality | Q2 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.issue | 45323 | en_US |
| dc.language.iso | en | en_US |
| dc.national | International | en_US |
| dc.numberofauthors | 1 | en_US |
| dc.pages | 40 - 53 | en_US |
| dc.relation.ispartof | Mathematical Logic Quarterly | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Residual Finiteness | en_US |
| dc.subject | Generalized Free Products | en_US |
| dc.subject | HNN Extension | en_US |
| dc.title | The space of minimal structures | en_US |
| dc.type | Article | en_US |
| dc.volume | 60 | en_US |
