The Maximal Cardinality of the Base in $ P_{2}\times P_{2} $

Malcev A. I. and Malcev I. A., Iterative Post Algebras [Russian], Nauka, Moscow (2012). Mirzoev R. J., “An expansion of functions of the algebra \( P_{k_{1}}\times\cdots\times P_{k_{m}} \) the algebra \( P(E_{2}^{2}) \) and the algebra of two valued functions over \( E_{2} \),” Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., vol. 24, no. 7, 143–146 (2004). Krnic L., “Cardinals of bases in the 3-valued logic. I,” Glasnik Mat., vol. 8, no. 2, 169–174 (1973). Malcev I. A. and Tugylbaeva B. G., “Products of iterative algebras,” Sib. Math. J., vol. 40, no. 1, 85–94 (1999). Marchenkov S. S., “On completeness in the system \( P_{3}\times P_{3} \),” Discrete Math. Appl., vol. 2, no. 6, 587–606 (1992). Marchenkov S. S., “On Slupecki classes in the systems \( P_{k}\times P_{l} \),” Discrete Math. Appl., vol. 3, no. 2, 147–160 (1993). Malcev I. A., Discrete Mathematics [Russian], Lan’, St. Petersburg (2011). Post E. L., “Introduction to a general theory of elementary propositions,” Amer. J. Math., vol. 43, no. 3, 163–185 (1921). Post E. L., The Two-Valued Iterative Systems of Mathematical Logic, Princeton Univ., Princeton (1941). Romov B. A., “On completeness in the square of functions of logic algebras and in the system \( P_{k}\times P_{l} \),” Cybernetics, vol. 4, no. 1, 9–14 (1987). Romov B. A., “A series of maximum subalgebras of direct products of algebras of finite-valued logics,” Cybernet. Systems Anal., vol. 25, no. 3, 300–306 (1989). Meshaik S., “Properties of linear functions from the algebra \( P_{2} \) and the functions do not belong into subalgebra defined by the relation \( R_{11} \) in \( P_{3}\times P_{3} \),” Izv. State Pedagogical University of Azerbaijan, vol. 2, 3–8 (2014).