  de Sitter cosmological horizons are known to exhibit thermodynamic properties
similar to black hole horizons. In this work we study causal set de Sitter
horizons, using Sorkin's spacetime entanglement entropy (SSEE) formula, for a
conformally coupled quantum scalar field. We calculate the causal set SSEE for
the Rindler-like wedge of a symmetric slab of de Sitter spacetime in $d=2,4$
spacetime dimensions using the Sorkin-Johnston vacuum state. We find that the
SSEE obeys an area law when the spectrum of the Pauli-Jordan operator is
appropriately truncated in both the de Sitter slab as well as its restriction
to the Rindler-like wedge. Without this truncation, the SSEE satisfies a volume
law. This is in agreement with Sorkin and Yazdi's calculations for the causal
set SSEE for nested causal diamonds in $\mathbb{M}^2$, where they showed that
an area law is obtained only after truncating the Pauli-Jordan spectrum. In
this work we explore different truncation schemes with the criterion that the
SSEE so obtained obeys an area law.
