Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the $n$-back-and-forth types of Boolean algebras
HTML articles powered by AMS MathViewer

by Kenneth Harris and Antonio Montalbán PDF
Trans. Amer. Math. Soc. 364 (2012), 827-866 Request permission

Abstract:

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.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 03D80, 03C57
  • Retrieve articles in all journals with MSC (2010): 03D80, 03C57
Additional Information
  • Kenneth Harris
  • Email: kenneth@kaharris.org
  • Antonio Montalbán
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1538
  • Email: antonio@math.uchicago.edu
  • 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: https://doi.org/10.1090/S0002-9947-2011-05331-6
  • MathSciNet review: 2846355