uppersemilattice

English

Alternative forms

• upper semilattice

Noun

uppersemilattice (plural uppersemilattices)

1. (mathematics) The upper subset of a semilattice
   • 2016, James Barnes, “On the decidability of the $\Sigma _{2}$ theories of the arithmetic and hyperarithmetic degrees as uppersemilattices”, in arXiv‎^[1]:

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