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I remember reading an article published in the 1970s by a Polish mathematician describing the first-order invariants of a torsion-free abelian group. I do not recollect the author's name, the title of the article or the publication.

Can anyone point me in the right direction?

(Not Ulm invariants, and definitely torsion-free)

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    $\begingroup$ Not Polish or 1970's, but Ulm invariants for groups sounds similar. Maybe look at papers citing Ulm? Gerhard "Maybe No Parentheses Were Used?" Paseman, 2017.11.09. $\endgroup$
    – Gerhard Paseman
    Commented Nov 10, 2017 at 6:10
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    $\begingroup$ OK. How about Eklof or Szmielew? Gerhard "Is Getting Warmer Or Colder?" Paseman, 2017.11.09. $\endgroup$
    – Gerhard Paseman
    Commented Nov 10, 2017 at 8:02
  • $\begingroup$ Thank you Gerhard "Is Getting Warmer Or Colder?" Paseman. I was out by 15 years but it was indeed $\endgroup$
    – Phill Schultz
    Commented Nov 11, 2017 at 7:37
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    $\begingroup$ Szmielew, W. (1955), "Elementary properties of Abelian groups", Fundamenta Mathematicae, 41: 203–271 $\endgroup$
    – Phill Schultz
    Commented Nov 11, 2017 at 8:06

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Szmielew, W. (1955), Elementary properties of Abelian groups, Fundamenta Mathematicae, 41: 203–271.

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  • $\begingroup$ BTW it addresses all abelian groups, not only torsion-free ones. Also, it does model theory without the modern language and without using ultrafilters. $\endgroup$
    – YCor
    Commented Jan 30, 2020 at 21:23
  • $\begingroup$ W is for Wanda. Her history also makes for an interesting read. Gerhard "Making My History Also Interesting" Paseman, 2020.01.30. $\endgroup$
    – Gerhard Paseman
    Commented Jan 30, 2020 at 21:36

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