@inproceedings { 5643, title = {A Representation Theorem for Finite Gödel Algebras with Operators}, booktitle = {26th Workshop on Logic, Language, Information and Computation, WoLLIC 2019}, volume = {11541}, year = {2019}, month = {02/07/2019}, pages = {223-235}, publisher = {Springer}, organization = {Springer}, edition = {R. Iemhoff et al.}, address = {Utrecht, The Netherlands}, abstract = {In this paper we introduce and study finite Godel algebras with operators (GAOs for short) and their dual frames. Taking into account that the category of finite Godel algebras with homomorphisms is dually equivalent to the category of finite forests with order-preserving open maps, the dual relational frames of GAOs are forest frames: finite forests endowed with two binary (crisp) relations satisfying suitable properties. Our main result is a Jonsson-Tarski like representation theorem for these structures. In particular we show that every finite Godel algebra with operators determines a unique forest frame whose set of subforests, endowed with suitably defined algebraic and modal operators, is a GAO isomorphic to the original one.}, keywords = {Finite Godel algebras, Modal operators, Finite forests. Representation theorem}, URL = {https://doi.org/10.1007/978-3-662-59533-6_14}, author = {Tommaso Flaminio and Llu\'{\i}s Godo and Ricardo Oscar Rodriguez} }