How can we Show that a set of axioms are independent?

Prasanth G. Narasimha-Shenoi @Prasanth_G_Narasimha-Shenoi2

05 May 2016 1 2K Report

I have a set of axioms. I want to prove each axiom is independent of others. I mean an axiom is not implied by a single axiom, or a combination of axioms. I think we need examples. If so how many?

Mihai Prunescu

I like the first answer by Peter Breuer. It was also the method used by Alfred Tarski to prove that the 7-axiom theory Q of arithmetic is built of independent axioms. He constructed 7 structures such that in any of them exactly one of the 7 axioms was false and the remaining 6 axioms were true. See "Undecidable theories" by Mostowski, R. M. Robinson and Tarski.

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