英和和英

名詞

uppersemilattice (複数形 uppersemilattices)

1. (mathematics) The upper subset of a semilattice
   • 2016, James Barnes, “On the decidability of the ${\displaystyle \Sigma _{2}}$ 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 ${\displaystyle {\mathcal {M}}}$ 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 ${\displaystyle {\mathcal {M}}}$.