This guide shows the location of all the collectibles (1 Spartan Cores, 2 UNSC Audio Log, 2 Banished Audio Log) in the Horn of Abolition in the Halo Infinite campaign.
Also Read: Halo Infinite Collectibles Guide
1) Spartan Core 1/1
It is inside a locked structure as shown in the picture below. Grapple to the top of the structure. You will find a hole at the top of the structure. Go inside through the hole to get the Spartan Core.
2) Banished Audio Log 1/2
Go inside the building north of the Spartan Core as shown in the picture below to get the audio log.
3) Banished Audio Log 2/2
Go inside the building as shown in the picture below to get the audio log.
4) UNSC Audio Log 1/2
Climb up the mountain southeast of the Horn of Abolition at the location shown in the picture below to get the audio log.
5) UNSC Audio Log 2/2
This one is on top of a rock along the path east of the Horn of Abolition as shown in the pictures below.