uppersemilattice

plural uppersemilattices · alternative upper semilattice

1. mathematicsThe upper subset of a semilattice

   1 more example

   This is achieved by using Kumabe-Slaman forcing - along with other known results - to show that given finite uppersemilattices #92;mathcal#123;M#125; and #92;mathcal#123;N#125;, where #92;mathcal#123;M#125; is a subuppersemilattice of #92;mathcal#123;N#125;, then for both degree structures, every embedding of #92;mathcal#123;M#125; into the structure extends to one of #92;mathcal#123;N#125; iff #92;mathcal#123;N#125; is an end-extension of #92;mathcal#123;M#125;.

   2016, James Barnes, “On the decidability of the Σ₂ theories of the arithmetic and hyperarithmetic degrees as uppersemilattices”, in arXiv