A unique column can be defined in a table by a unique constraint or unique index. Oracle standard allows multiple nulls in a unique column, and that is how PostgreSQL behaves. Both single column and composite unique index behave similar in Oracle and PostgreSQL database.
OraclePostgreSQL
CREATE TABLE null_test(
tid NUMBER,
tname VARCHAR2(10),
tdate DATE
);
ALTER TABLE null_test ADD CONSTRAINT null_test_unq UNIQUE(tid);
INSERT INTO null_test VALUES(1, 'test-1', current_date);
INSERT INTO null_test VALUES(NULL, 'test-n1', current_date);
INSERT INTO null_test VALUES(NULL, 'test-n2', current_date);
INSERT INTO null_test VALUES(NULL, 'test-n3', current_date);
commit;CREATE TABLE null_test(
tid INTEGER,
tname VARCHAR(10),
tdate DATE
);
ALTER TABLE null_test ADD CONSTRAINT null_test_unq UNIQUE(tid);
INSERT INTO null_test VALUES(1, 'test-1', current_date);
INSERT INTO null_test VALUES(NULL, 'test-n1', current_date);
INSERT INTO null_test VALUES(NULL, 'test-n2', current_date);
INSERT INTO null_test VALUES(NULL, 'test-n3', current_date);