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MoeBlee wrote:
> Here's one that has me stumped:
>
> In ZR(-I) (that's Z set theory with the axiom of regularity but not the
> axiom of infinity), prove:
>
> bXc = b -> b=0
>
> where 'X' stands for the Cartesian product.
>
> You may not use the 'infinite sequence of nested members' version of
> regularity. But the following previous theorems are available (where
> 'e' stands for 'is a member of') along with the usual "first chapter"
> theorems of set theory:
>
> ~SeS
>
> ~SeTeS
>
> ~SeTeVeS
>
> S subset SXS -> S=0
>
How do you prove this one with regularity but not infinity?
> Source: 'Axiomatic Set Theory' by Suppes, pg. 56, exercise 2 (Dover
> edition).
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