Intuitionistic set theory: or how to construct semi-rings. Part III (Q2753393)

See the review of Part I and the announcement of Part II (Verlag Dr. Kovač, Hamburg, 1998) in Zbl 0924.03101 and Zbl 0979.03041, respectively.NEWLINENEWLINENEWLINE Publisher's description: Hilbert's Program is completed by a finite method, which constructs propositions. The constructed propositions can make assertions about infinitive sets. Intuitionistic Set Theory generalizes the construction of an algebraic-real number u. u is a complex number, which satisfies a polynomial equation with rational coefficients not all zero: \(a_0 + a_1u + a_2u^2 +\dots - a_{n-1}u^{n-1} + a_nu^n = 0\) \((a_i\;\text{in} Q,\;\text{not all} a_i=0).\) NEWLINENEWLINENEWLINEA proof is an eigenvector in a Banach-semi-space, which satisfies its characteristic polynominal \((\lambda_1-\lambda) (\lambda_2-\lambda) \dots (\lambda_{n-1}-\lambda) (\lambda_n-\lambda) = 0.\) NEWLINENEWLINENEWLINEThe eigenvalues \(\lambda_i\) are constructed by a proof. A proof is a regular endomorphism. Intuitionistic Set Theory uses for the calculation of a semi-ring known propositions (operators). This Part III generalizes Group-Theory.