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Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the settheoretic relationships between these classes of trees and between their corresponding firstorder theories. We then obtain some general results about the axiomatization of the firstorder theories of some of these classes of trees in terms of (...) 

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions have been considered and axiomatic systems which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, we use (...) 

We present an extension of the mosaic method aimed at capturing manydimensional modal logics. As a proofofconcept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness (...) 