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Ali Enayat
Ali Enayat
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In my hasty first reading I did not notice the stipulation about parameter-freeness; I am leaving this answer "only for the record".

The answer to the question is in the positive (provided, provided "real ordered field" is interpreted as "real closed field"), and parameters are allowed.

  The details are worked out in a section 3 of a paper by Salehi and Zarza (a preprint of which can be found here); the paper was published as follows:

S. Salehi & M. Zarza, First-Order Continuous Induction and a Logical Study of Real Closed Fields, Bulletin of the Iranian Mathematical Society volume 46, pages225–243(2020).

The answer to the question is in the positive (provided "real ordered field" is interpreted as "real closed field").

  The details are worked out in a section 3 of a paper by Salehi and Zarza (a preprint of which can be found here); the paper was published as follows:

S. Salehi & M. Zarza, First-Order Continuous Induction and a Logical Study of Real Closed Fields, Bulletin of the Iranian Mathematical Society volume 46, pages225–243(2020).

In my hasty first reading I did not notice the stipulation about parameter-freeness; I am leaving this answer "only for the record".

The answer to the question is in the positive, provided "real ordered field" is interpreted as "real closed field", and parameters are allowed. The details are worked out in a section 3 of a paper by Salehi and Zarza (a preprint of which can be found here); the paper was published as follows:

S. Salehi & M. Zarza, First-Order Continuous Induction and a Logical Study of Real Closed Fields, Bulletin of the Iranian Mathematical Society volume 46, pages225–243(2020).

Source Link
Ali Enayat
Ali Enayat
  • 17.7k
  • 2
  • 63
  • 105

The answer to the question is in the positive (provided "real ordered field" is interpreted as "real closed field").

The details are worked out in a section 3 of a paper by Salehi and Zarza (a preprint of which can be found here); the paper was published as follows:

S. Salehi & M. Zarza, First-Order Continuous Induction and a Logical Study of Real Closed Fields, Bulletin of the Iranian Mathematical Society volume 46, pages225–243(2020).