preprintCommunications of the American Mathematical SocietyJan 29, 2026HYBRID OA

Existential characterizations of monadic NIP

SBSamuel BraunfeldMLM. Laskowski

Czech Academy of Sciences, Institute of Computer Science · University of Maryland, College Park

Indexed inarxivcrossrefdatacite

Abstract

We show that if a universal theory is not monadically NIP, then this is witnessed by a canonical configuration defined by an existential formula. As a consequence, we show that a hereditary class of relational structures is NIP (resp. stable) if and only if it is monadically NIP (resp. monadically stable). As another consequence, we show that if such a class is not monadically NIP, then it has superexponential growth rate.

Citation impact

5
total citations
FWCI
0.00
Percentile
96%
References
16
Citations per year

Authors

2

Topics & keywords

Topics
Keywords
  • NIP
  • Class (philosophy)
  • Existentialism
  • Mathematics
  • Pure mathematics
  • Discrete mathematics
  • Computer science
  • Philosophy
No related works found for this paper.

Funding