"Alien objects", Stillwell's "Reverse Mathematics"

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TL;DR
What is an example of "alien objects" allowed by the first four Peano axioms?
Stillwell's "Reverse Mathematics" says on p.41,

1768489825029.webp


Unfortunately, there is no example of such model. Where can I find it?

For the reference, here are the axioms 1-4:

1768489947553.webp

1768489973673.webp
 

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