diff --git a/core/set.rbs b/core/set.rbs
index 87af3ce5c..1443f85ce 100644
--- a/core/set.rbs
+++ b/core/set.rbs
@@ -414,6 +414,15 @@ class Set[unchecked out A]
   #
   def compare_by_identity: () -> self
 
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - compare_by_identity?()
+  # -->
+  # Returns true if the set will compare its elements by their
+  # identity. Also see Set#compare_by_identity.
+  #
+  def compare_by_identity?: () -> bool
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - disjoint?(set)
@@ -477,6 +486,15 @@ class Set[unchecked out A]
   #
   def flatten: () -> Set[untyped]
 
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - flatten!()
+  # -->
+  # Equivalent to Set#flatten, but replaces the receiver with the
+  # result in place. Returns nil if no modifications were made.
+  #
+  def flatten!: () -> self?
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - intersect?(set)
@@ -532,6 +550,13 @@ class Set[unchecked out A]
   #
   def subset?: (self) -> bool
 
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - <=(set)
+  # -->
+  #
+  alias <= subset?
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - proper_subset?(set)
@@ -540,6 +565,13 @@ class Set[unchecked out A]
   #
   def proper_subset?: (self) -> bool
 
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - <(set)
+  # -->
+  #
+  alias < proper_subset?
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - superset?(set)
@@ -548,6 +580,13 @@ class Set[unchecked out A]
   #
   def superset?: (self) -> bool
 
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - >=(set)
+  # -->
+  #
+  alias >= superset?
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - proper_superset?(set)
@@ -556,6 +595,13 @@ class Set[unchecked out A]
   #
   def proper_superset?: (self) -> bool
 
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - >(set)
+  # -->
+  #
+  alias > proper_superset?
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - replace(enum)
@@ -587,6 +633,11 @@ class Set[unchecked out A]
   #
   def select!: () { (A) -> untyped } -> self?
 
+  # <!-- rdoc-file=lib/set.rb -->
+  # Equivalent to Set#select!
+  #
+  alias filter! select!
+
   # <!--
   #   rdoc-file=lib/set.rb
   #   - subtract(enum)
@@ -605,6 +656,15 @@ class Set[unchecked out A]
   #     Set[1, 'c', :s].to_a              #=> [1, "c", :s]
   #
   def to_a: () -> Array[A]
+
+  # <!--
+  #   rdoc-file=lib/set.rb
+  #   - join(separator=nil)
+  # -->
+  # Returns a string created by converting each element of the set to a string
+  # See also: Array#join
+  #
+  def join: (?string separator) -> String
 end
 
 %a{annotate:rdoc:skip}