Abstract

We present a collection of fixed point theorems in the framework of finitely supported structures, preserving the validity of several classical Zermelo-Fraenkel fixed point theorems such as Tarski strong theorem, Bourbaki-Witt theorem, Scott theorem and Tarski-Kantorovitch theorem. We also prove several specific fixed point properties in the framework of finitely supported algebraic structures, results that are not reformulations of some corresponding Zermelo-Fraenkel results. Applications of the fixed point theorems are emphasized by presenting many examples of finitely supported ordered structures for which these theorems can be used. Particularly, the results provide properties of L-fuzzy sets defined in the world of finitely supported structures.

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