superlimit

From super- +‎ limit.

• Audio (US):

  (file)

superlimit (plural superlimits)

1. (mathematics) A superstable limit
   • 2015, Rami Grossberg, Sebastien Vasey, “Superstability in abstract elementary classes”, in arXiv‎:

     Then the following are equivalent: 1) For all high-enough ${\displaystyle \lambda }$, there exists ${\displaystyle \kappa \leq \lambda }$ such that there is a good ${\displaystyle \lambda }$-frame on the class of ${\displaystyle \kappa }$-saturated models in ${\displaystyle K_{\lambda }}$. 2) For all high-enough ${\displaystyle \lambda }$, ${\displaystyle K}$ has a unique limit model of cardinality ${\displaystyle \lambda }$. 3) For all high-enough ${\displaystyle \lambda }$, ${\displaystyle K}$ has a superlimit model of cardinality ${\displaystyle \lambda }$. 4) For all high-enough ${\displaystyle \lambda }$, the union of a chain of ${\displaystyle \lambda }$-saturated models is ${\displaystyle \lambda }$-saturated. 5) There exists ${\displaystyle \theta }$ such that for all high-enough ${\displaystyle \lambda }$, ${\displaystyle K}$ is ${\displaystyle (\lambda ,\theta )}$-solvable..