Year: 1975
Type: article
Abstract: In this note we remark that the Tarski-Bernays and Frege systems which are obtained by H. Hiz in his C-calculus presentation [l] can be obtained in fewer theorems. In the beginning we consider the first 15 theses, the same ones that are in [1], then the derivation is made in the following way: 11 p/Cpq, q/Cqr, r/CprX C13-16 16. CCqrCCpqCpr 13 p/Csq, q/CCqrCsr, r/CCpCqrCpCsrX C13 p/s-C16 q/Cqr, r/Csr-17 17. CCsqCCpCqrCpCsr 11 p/Csq, q/CpCqr, r/CpCqr X C17-18 18. CCpCqrCCsqCpCsr 13 p/Crs, q/CCqrCqs, r/CCpCqrCpCqs X C16 p/q, q/r, r/s-C16 q/Cqr, r/Cqs-19 19. CCrsCCpCqrCpCqs 19 p/CpCqr, q/Cpq, r/CpCpr, s/Cpr x C8 q/r-CIS s/p-20 20. CCpCqrCCpqCpr 4, 15, 13 form the Tarski-Bernays system and 4, 20 form the Frege system (in [l] 4, 33). We remark also that the deduction theorem can be proved without using thesis 20 (see
Author: Constantin Milici
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2008744481