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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the $n$-back-and-forth types of Boolean algebras
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by Kenneth Harris and Antonio Montalbán PDF
Trans. Amer. Math. Soc. 364 (2012), 827-866 Request permission


The objective of this paper is to uncover the structure of the back-and-forth equivalence classes at the finite levels for the class of Boolean algebras. As an application, we obtain bounds on the computational complexity of determining the back-and-forth equivalence classes of a Boolean algebra for finite levels. This result has implications for characterizing the relatively intrinsically $\Sigma ^0_n$ relations of Boolean algebras as existential formulas over a finite set of relations.
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Additional Information
  • Kenneth Harris
  • Email:
  • Antonio Montalbán
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1538
  • Email:
  • Received by editor(s): October 2, 2007
  • Received by editor(s) in revised form: January 28, 2008, August 13, 2008, June 9, 2009, June 29, 2009, February 18, 2010, and February 19, 2010
  • Published electronically: September 1, 2011
  • Additional Notes: The second author was partially supported by NSF Grants DMS-0600824 and DMS-0901169 and by the Marsden Foundation of New Zealand, via a postdoctoral fellowship
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 827-866
  • MSC (2010): Primary 03D80; Secondary 03C57
  • DOI:
  • MathSciNet review: 2846355