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In NBG with global choice, No is (up to isomorphism) the unique homogeneous universal ordered field, i.e. it contains an isomorphic copy of every ordered field whose universe is a set or proper class of NBG, and every isomorphism between subfields of No, whose universe are sets, can be extended to an automorphism. The proof that No contains an isomorphic copy of every ordered field of power On uses global choice as does the proof of homogeneity. It is not clear to me how one can prove either of these results about the Kanovei-Reeken system in the Kanovei-Reeken framework. Of course, I may not be thinking creatively enough; moreover, it might be possible that Vladimir's first question would have a positive answer for some pared down version of No, but based on a private exchange with Vladimir as well as his question, it's No of Theorem 20 he has in mind.

In NBG with global choice, No is (up to isomorphism) the unique homogeneous universal ordered field, i.e. it contains an isomorphic copy of every ordered field whose universe is a set or proper class of NBG, and every isomorphism between subfields of No, whose universes are sets, can be extended to an automorphism. The proof that No contains an isomorphic copy of every ordered field of power On uses global choice as does the proof of homogeneity. It is not clear to me how one can prove either of these results about the Kanovei-Reeken system in the Kanovei-Reeken framework. Of course, I may not be thinking creatively enough; moreover, it might be possible that Vladimir's first question would have a positive answer for some pared down version of No, but based on a private exchange with Vladimir as well as his question, it's No of Theorem 20 he has in mind.

In NBG with global choice, No is (up to isomorphism) the unique homogeneous universal ordered field, i.e. it contains an isomorphic copy of every ordered field whose universe is a set or proper class of NBG, and every isomorphism between subfields of No, whose universe are sets, can be extended to an automorphism. The proof that No contains an isomorphic copy of every ordered field of power On uses global choice as does the proof of homogeneity. It is not clear to me how one can prove either of these results about the Kanovei-Reeken system in the Kanovei-Reeken framework. In fact, every way I can think of to even prove it contains an isomorphic copy of No uses a proper class of choices. Of course, I may not be thinking creatively enough; moreover, it might be possible that Vladimir's first question would have a positive answer for some pared down version of No, but based on a private exchange with Vladimir as well as his question, it's No of Theorem 20 he has in mind.

In NBG with global choice, No is (up to isomorphism) the unique homogeneous universal ordered field, i.e. it contains an isomorphic copy of every ordered field whose universe is a set or proper class of NBG, and every isomorphism between subfields of No, whose universe are sets, can be extended to an automorphism. The proof that No contains an isomorphic copy of every ordered field of power On uses global choice as does the proof of homogeneity. It is not clear to me how one can prove either of these results about the Kanovei-Reeken system in the Kanovei-Reeken framework. Of course, I may not be thinking creatively enough; moreover, it might be possible that Vladimir's first question would have a positive answer for some pared down version of No, but based on a private exchange with Vladimir as well as his question, it's No of Theorem 20 he has in mind.

In NBG with global choice, No is (up to isomorphism) the unique homogeneous universal ordered field, i.e. it contains an isomorphic copy of every ordered field whose universe is a set or proper class of NBG, and every isomorphism between subfields of No, whose universe are sets, can be extended to an automorphism. The proof that No contains an isomorphic copy of every ordered field of power On uses global choice as does the proof of homogeneity. It is not clear to me how one can prove either of these results about the Kanovei-Reeken system in the Kanovei-Reeken framework. In fact, every way I can think of to even prove it contains an isomorphic copy of No uses a proper class of choices. Of course, I may not be thinking creatively enough.

In NBG with global choice, No is (up to isomorphism) the unique homogeneous universal ordered field, i.e. it contains an isomorphic copy of every ordered field whose universe is a set or proper class of NBG, and every isomorphism between subfields of No, whose universe are sets, can be extended to an automorphism. The proof that No contains an isomorphic copy of every ordered field of power On uses global choice as does the proof of homogeneity. It is not clear to me how one can prove either of these results about the Kanovei-Reeken system in the Kanovei-Reeken framework. In fact, every way I can think of to even prove it contains an isomorphic copy of No uses a proper class of choices. Of course, I may not be thinking creatively enough; moreover, it might be possible that Vladimir's first question would have a positive answer for some pared down version of No, but based on a private exchange with Vladimir as well as his question, it's No of Theorem 20 he has in mind.