subuppersemilattice

From sub- +‎ uppersemilattice.

subuppersemilattice (plural subuppersemilattices)

1. (mathematics) A sub-semilattice of an uppersemilattice.
   • 1988, Manuel Lerman, Richard A. Shore-, “Decidability and invariant classes for degree structures”, in Transactions of the American Mathematical Society, volume 310, number 2:

     First, given any finite subuppersemilattice U ot 3 with top element 0' and an isomorphism type V of a poset extending U consistently with its structure as an usl such that V and U have the same top element and V is an end extension of ...

   • 2016, James Barnes, “On the decidability of the ${\displaystyle \Sigma _{2}}$ theories of the arithmetic and hyperarithmetic degrees as uppersemilattices”, in arXiv‎:

     This is achieved by using Kumabe-Slaman forcing - along with other known results - to show that given finite uppersemilattices ${\displaystyle {\mathcal {M}}}$ and ${\displaystyle {\mathcal {N}}}$, where ${\displaystyle {\mathcal {M}}}$ is a subuppersemilattice of ${\displaystyle {\mathcal {N}}}$, then for both degree structures, every embedding of ${\displaystyle {\mathcal {M}}}$ into the structure extends to one of ${\displaystyle {\mathcal {N}}}$ iff ${\displaystyle {\mathcal {N}}}$ is an end-extension of ${\displaystyle {\mathcal {M}}}$..