diff --git a/stdlib/set/0/set.rbs b/stdlib/set/0/set.rbs
index 11c15242e..baf3680f3 100644
--- a/stdlib/set/0/set.rbs
+++ b/stdlib/set/0/set.rbs
@@ -423,6 +423,15 @@ class Set[unchecked out A]
   #
   def reject!: () { (A) -> untyped } -> self
 
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - compare_by_identity()
+  # -->
+  # Makes the set compare its elements by their identity and returns
+  # self. This method may not be supported by all subclasses of Set.
+  #
+  def compare_by_identity: () -> self
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - disjoint?(set)
@@ -467,6 +476,7 @@ class Set[unchecked out A]
   # given.
   #
   def each: () { (A) -> void } -> self
+          | () -> Enumerator[A, self]
 
   # <!--
   #   rdoc-file=lib/set.rb
diff --git a/test/stdlib/set/Set_test.rb b/test/stdlib/set/Set_test.rb
new file mode 100644
index 000000000..e0d8fff84
--- /dev/null
+++ b/test/stdlib/set/Set_test.rb
@@ -0,0 +1,29 @@
+require_relative "../test_helper"
+
+require "set"
+
+class SetTest < Test::Unit::TestCase
+  include TypeAssertions
+
+  library "set"
+  testing "::Set[::Integer]"
+
+  def test_each
+    assert_send_type(
+      "() -> ::Enumerator[::Integer, ::Set[::Integer]]",
+      Set[1], :each
+    )
+
+    assert_send_type(
+      "() { (::Integer) -> ::Integer } -> ::Set[::Integer]",
+      Set[1], :each
+    ) do |x| x+1 end
+  end
+
+  def test_compare_by_identity
+    assert_send_type(
+      "() -> ::Set[::Integer]",
+      Set[1], :compare_by_identity
+    )
+  end
+end