Geodesic
Infinitely many maximal primitive positive clones in a diagonalizable algebra
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 47-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a rather simple example of infinitely many maximal primitive positive clones in a diagonalizable algebra, which serve as an algebraic model for the provability propositional logic $GL$. 
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     author = {Andrei Rusu},
     title = {Infinitely many maximal primitive positive clones in a~diagonalizable algebra},
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Andrei Rusu. Infinitely many maximal primitive positive clones in a diagonalizable algebra. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 47-52. http://geodesic.mathdoc.fr/item/BASM_2013_2_a5/

[1] Burris S., Willard R., “Finitely many primitive positive clones”, Proceedings of the American Mathematical Society, 101:3 (1987), 427–430 | DOI | MR | Zbl

[2] Szabo L., “On the lattice of clones acting bicentrally”, Acta Cybernet., 6 (1984), 381–388 | MR

[3] Kuznetsov A. V., “On detecting non-deducibility and non-expressibility”, Locical deduction, Nauka, Moscow, 1979, 5–33 (in Russian)

[4] Danil'c̆enco A. F., “Parametric expressibility of functions of three-valued logic”, Algebra i Logika, 16 (1977), 397–416 (in Russian) | MR | Zbl

[5] Magari R., “The diagonalizable algebras (the algebraization of the theories which express Theor.): II”, Boll. Unione Mat. Ital., 12, Suppl. fasc. 3 (1975), 117–125 | MR | Zbl

[6] Solovay R. M., “Provability interpretations of modal logic”, Israel J. Math., 25 (1975), 287–304 | DOI | MR

[7] Szendrei Á., Clones in universal algebra, Séminaire de Mathématiques Supérieures, 99, Les Presses de l'Université de Montréal, 1986 | MR | Zbl

[8] Szabó L., “On algebras with primitive positive clones”, Acta Sci. Math. (Szeged), 73 (2007), 463–470 | MR | Zbl

[9] Danil'c̆enco A. F., “On parametrical expressibility of the functions of $k$-valued logic”, Colloq. Math. Soc. Janos Bolyai, 28, North-Holland, 1981, 147–159 | MR