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

Genady
in Mathematics

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Stillwell's "Reverse Mathematics" says on p.41,

Screenshot 2026-01-15 110246.png

Unfortunately, there is no example of such model. Does anybody know such?

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

Screenshot 2026-01-15 111223.png

Screenshot 2026-01-15 111249.png

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