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axiomatics

solakis

Active member
Dec 9, 2012
304
Given :

A) primitive symbols : (1, *) and

B) The axioms:

1) \(\displaystyle \forall x\forall y[x*=y*\Longrightarrow x=y]\)

2) \(\displaystyle \forall x[x*\neq 1]\)

3) \(\displaystyle [P(1)\wedge\forall x(P(x)\Longrightarrow P(x*))]\Longrightarrow\forall xP(x)\)

Then prove:

\(\displaystyle \forall x[x=1\vee \exists y(y*=x)]\)