Fraenkel/Mostowski Models

Abstract

Let R(x, y) be a relation of two arguments that establishes a bijection from the universe U on to itself; that is, a relation which satisfies the following conditions:

$$\forall x\forall y\forall y'\left[ {R\left( {x,y} \right) \wedge R\left( {x,y'} \right) \to y = y'} \right];$$

$$\forall x\forall x'\forall y\left[ {R\left( {x,y} \right) \wedge R\left( {x,y'} \right) \to x = x'} \right]; $$

$$\forall x\exists yR\left( {x,y} \right) \wedge \forall y\exists xR\left( {x,y} \right) $$

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