Preservation theorems in {\L}ukasiewicz \\model theory

Document Type: Research Paper


1 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

2 Department of Mathematics, Shahid Beheshti University, G. C., Evin, Tehran, Iran


We present some model theoretic results for {\L}ukasiewicz
predicate logic by using the methods of continuous model theory
developed by Chang and Keisler.
We prove compactness theorem with respect to the class of all
structures taking values in the {\L}ukasiewicz $\texttt{BL}$-algebra.
We also prove some appropriate preservation theorems concerning universal and inductive theories.
Finally, Skolemization and Morleyization in this framework are discussed and
some natural examples of fuzzy theories are presented.


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