TY - JOUR JF - IJMSI JO - IJMSI VL - 17 IS - 2 PY - 2022 Y1 - 2022/9/01 TI - Linear Formulas in Continuous Logic TT - 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. SP - 75 EP - 86 AU - Bagheri, S. M. AU - Fadai, F. AD - Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran KW - Continuous logic KW - Ultramean KW - Linear formula KW - $Sigma_n$-formula KW - Positive formula. UR - http://ijmsi.ir/article-1-1420-en.html DO - 10.52547/ijmsi.17.2.75 ER -