How do I set a default value for a UUID primary key column in Postgres?

In order to use uuid_generate_v4(), you first need to execute:

CREATE EXTENSION IF NOT EXISTS "uuid-ossp";

If the column id already exists in the table and you want to modify it by making it the primary key and adding a default value, you can do it in 2 steps:

ALTER TABLE my_object_times ADD PRIMARY KEY (id);
ALTER TABLE my_object_times ALTER COLUMN id SET DEFAULT uuid_generate_v4();

If the column doesn't exist at all, then you can create it with all the attributes you want, by simply doing:

ALTER TABLE my_object_times ADD id uuid PRIMARY KEY DEFAULT uuid_generate_v4();

(I cannot test this right now but it should work)