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The isomorphism theorem for linear fragments of continuous logic
Author(s) -
Bagheri SeyedMohammad
Publication year - 2021
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.202000044
Subject(s) - ultraproduct , mathematics , isomorphism (crystallography) , pure mathematics , discrete mathematics , isomorphism extension theorem , algebra over a field , picard–lindelöf theorem , fixed point theorem , chemistry , crystal structure , crystallography
The ultraproduct construction is generalized to p ‐ultramean constructions ( 1 ⩽ p < ∞ ) by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments L p of continuous logic and are very close to theL p ( R )constructions in real analysis. A powermean variant of the Keisler‐Shelah isomorphism theorem is proved for L p . It is then proved that L p ‐sentences (and their approximations) are exactly those sentences of continuous logic which are preserved by such constructions. Some other applications are also given.