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

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

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

See also

References

Created on May 3, 2022 at 19:28:50. See the history of this page for a list of all contributions to it.