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A local characterization of VC-minimality


Authors: Uri Andrews and Vincent Guingona
Journal: Proc. Amer. Math. Soc. 144 (2016), 2241-2256
MSC (2010): Primary 03C45, 03C57, 03D80
DOI: https://doi.org/10.1090/proc/12805
Published electronically: January 27, 2016
MathSciNet review: 3460182
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Abstract: We show VC-minimality is $ \Pi ^0_4$-complete. In particular, we give a local characterization of VC-minimality. We also show dp-smallness is $ \Pi ^1_1$-complete.


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Additional Information

Uri Andrews
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
Email: andrews@math.wisc.edu

Vincent Guingona
Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, Indiana 46556
Address at time of publication: Department of Mathematics, Ben-Gurion University of teh Negev, Be’er Sheva, Israel 8410501
Email: guingona@math.bgu.ac.il

DOI: https://doi.org/10.1090/proc/12805
Received by editor(s): July 22, 2014
Received by editor(s) in revised form: March 21, 2015
Published electronically: January 27, 2016
Additional Notes: The first author’s research was partially supported by NSF grant DMS-1201338. The second author’s research was supported by NSF grant DMS-0838506. This material is based upon work supported by the NSF under grant no. 0932078000 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2014 semester.
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society