TY - JOUR
T1 - Linear Formulas in Continuous Logic
TT -
JF - IJMSI
JO - IJMSI
VL - 17
IS - 2
UR - http://ijmsi.ir/article-1-1420-en.html
Y1 - 2022
SP - 75
EP - 86
KW - Continuous logic
KW - Ultramean
KW - Linear formula
KW - $Sigma_n$-formula
KW - Positive formula.
N2 - We prove that continuous sentences preserved by the ultramean construction (a generalization of the ultraproduct construction) are exactly those sentences which are approximated by linear sentences. Continuous sentences preserved by linear elementary equivalence are exactly those sentences which are approximated in the Riesz space generated by linear sentences. Also, characterizations for linear $Delta_n$-sentences and positive linear theories will be given.
M3 10.52547/ijmsi.17.2.75
ER -