The field F8 as a Boolean manifold
نویسندگان
چکیده
In a previous paper (“Hexagonal Logic of the Field F8 as a Boolean Logic with Three Involutive Modalities”, in The road to Universal Logic), we proved that elements of P(8), i.e. functions of all finite arities on the Galois field F8, are compositions of logical functions of a given Boolean structure, plus three geometrical cross product operations. Here we prove that P(8) admits a purely logical presentation, as a Boolean manifold, generated by a diagram of 4 Boolean systems of logical operations on F8. In order to obtain this result we provide various systems of parameters of the set of unordered bases on F2, and consequently parametrical polynomial expressions for the corresponding conjunctions, which in fact are enough to characterize these unordered bases (and the corresponding Boolean structures). 2010 Mathematics Subject Classification. 03B50. 03G05, 06Exx, 06E25, 06E30, 11Txx.
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