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, Skolemization and Morleyization in this framework are discussed andsome natural examples of fuzzy theories are presented.

Keywords:

Continuous model theory , {L}ukasiewicz logic , Preservation theorems