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...

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...

We present new preservation theorems that semantically characterize the ∃∀ and ∀∃ prefix classes of first order logic, for each natural number k. Unlike preservation theorems in the literature that characterize the ∃∗∀∗ and ∀∗∃∗ prefix classes, our theorems relate the count of quantifiers in the leading block of the quantifier prefix to natural quantitative properties of the models. As special ...

The class of all MTL-algebras is a variety, denoted MTL. Alternatively, an MTL-algebra is a representable, commutative, integral residuated lattice with a least element.

In this paper we naturally define when a theory has bounded quantifier elimination, or is bounded model complete. We give several equivalent conditions for a theory to have each of these properties. These results provide simple proofs for some known results in the model theory of the bounded arithmetic theories like CPV and PV1. We use the mentioned results to obtain some independence results i...