The lattice of sets of natural numbers is rich
$\newcommand\of{\subseteq}\newcommand\N{\mathbb{N}}\newcommand\R{\mathbb{R}}\def\{\left\langle#1\right\rangle}\newcommand\Z{\mathbb{Z}}\newcommand\Q{\mathbb{Q}}\newcommand\ltomega{{{<}\omega}}\newcommand\unaryminus{-}\newcommand\intersect{\cap}\newcommand\union{\cup}\renewcommand\emptyset{\varnothing}$Let us explore the vast and densely populated expanses of the lattice of all sets of natural numbers—the power set lattice $\$. We find in this lattice every possible set of natural numbers $A\of\N$, and we consider them with respect to the subset relation $A\of B$. This is a lattice order because the union of … Devamını oku