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Ultrafilter extensions do not preserve elementary equivalence
Author(s) -
Saveliev Denis I.,
Shelah Saharon
Publication year - 2019
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201900045
Subject(s) - ultrafilter , mathematics , equivalence (formal languages) , calculus (dental) , mathematics education , pure mathematics , discrete mathematics , medicine , dentistry
We show that there are models M 1 and M 2 such that M 1 elementarily embeds into M 2 but their ultrafilter extensions ββ ( M 1 ) and ββ ( M 2 ) are not elementarily equivalent.