Seyed-Mohammad Bagheri
Department of Pure Mathematics, Faculty of Mathemat- ical Sciences, Tarbiat Modares University, P.O. Box 14115-134, and Institute for Re- search in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
[ 1 ] - Preservation theorems in {L}ukasiewicz \model theory
We present some model theoretic results for {L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {L}ukasiewicz $texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemizatio...
[ 2 ] - On the Ultramean Construction
We use the ultramean construction to prove linear compactness theorem. We also extend the Rudin-Keisler ordering to maximal probability charges and characterize it by embeddings of power ultrameans.
[ 3 ] - Linear Formulas in Continuous Logic
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 linea...
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