nLab sigma-complete lattice

Contents

Contents

Definition

A σ\sigma-complete lattice is a lattice (L,,,,,)(L, \leq, \bot, \vee, \top, \wedge) with a function

i:()(i):(L)L\Vee_{i:\mathbb{N}} (-)(i): (\mathbb{N} \to L) \to L

such that

  • for all natural numbers nn \in \mathbb{N} and sequences s:Ls: \mathbb{N} \to L

    s(n) i:s(i) s(n) \leq \Vee_{i:\mathbb{N}} s(i)
  • for all elements xLx \in L and sequences s:Ls: \mathbb{N} \to L, if s(n)xs(n) \leq x for all natural numbers nn \in \mathbb{N}, then

    i:s(i)x\Vee_{i:\mathbb{N}} s(i) \leq x

See also

References

Last revised on June 11, 2024 at 16:55:28. See the history of this page for a list of all contributions to it.