We construct the finitely generated free algebras and determine the free spectra of varieties of linear equivalential algebras and linear equivalential algebras of finite height corresponding, respectively, to the equivalential fragments of intermediate Gödel-Dummett logic and intermediate finite-valued logics of Gödel. Thus we compute the number of purely equivalential propositional formulas in these logics in n variables for an arbitrary n∈ℕ.
"Free spectra of linear equivalential algebras." J. Symbolic Logic 70 (4) 1341 - 1358, December 2005. https://doi.org/10.2178/jsl/1129642128