diff --git a/stdlib/public/core/SetAlgebra.swift b/stdlib/public/core/SetAlgebra.swift
index 822d5bc..9386cd5 100644
--- a/stdlib/public/core/SetAlgebra.swift
+++ b/stdlib/public/core/SetAlgebra.swift
@@ -20,7 +20,7 @@
 /// In a model of `SetAlgebra`, some elements may subsume other
 /// elements, where
 ///
-/// > `a` **subsumes** `b` iff `([a] as Self).isSupersetOf([b])`
+/// > `a` **subsumes** `b` iff `([a] as Self).isSuperset(of: [b])`
 ///
 /// In many models of `SetAlgebra` such as `Set<Element>`, `a`
 /// *subsumes* `b` if and only if `a == b`, but that is not always the
@@ -35,16 +35,16 @@
 ///   of type `S`, and `e` is of type `S.Element`:
 ///
 ///   - `S() == []`
-///   - `x.intersect(x) == x`
-///   - `x.intersect([]) == []`
-///   - `x.union(x) == x`
-///   - `x.union([]) == x`
+///   - `x.intersection(with: x) == x`
+///   - `x.intersection(with: []) == []`
+///   - `x.unioning(with: x) == x`
+///   - `x.unioning(with: []) == x`
 ///   - `x.contains(e)` implies `x.union(y).contains(e)`
-///   - `x.union(y).contains(e)` implies `x.contains(e) || y.contains(e)`
-///   - `x.contains(e) && y.contains(e)` iff `x.intersect(y).contains(e)`
-///   - `x.isSubsetOf(y)` iff `y.isSupersetOf(x)`
-///   - `x.isStrictSupersetOf(y)` iff `x.isSupersetOf(y) && x != y`
-///   - `x.isStrictSubsetOf(y)` iff `x.isSubsetOf(y) && x != y`
+///   - `x.unioning(with: y).contains(e)` implies `x.contains(e) || y.contains(e)`
+///   - `x.contains(e) && y.contains(e)` iff `x.intersection(with: y).contains(e)`
+///   - `x.isSubset(of: y)` iff `y.isSuperset(of: x)`
+///   - `x.isStrictSuperset(of: y)` iff `x.isSuperset(of: y) && x != y`
+///   - `x.isStrictSubset(of: y)` iff `x.isSubset(of: y) && x != y`
 public protocol SetAlgebra : Equatable, ArrayLiteralConvertible {
   /// A type for which `Self` provides a containment test.
   associatedtype Element
@@ -63,16 +63,16 @@ public protocol SetAlgebra : Equatable, ArrayLiteralConvertible {
   /// Returns the set of elements contained in `self`, in `other`, or in
   /// both `self` and `other`.
   @warn_unused_result
-  func union(other: Self) -> Self
+  func unioning(with other: Self) -> Self

   /// Returns the set of elements contained in both `self` and `other`.
   @warn_unused_result
-  func intersect(other: Self) -> Self
+  func intersection(with other: Self) -> Self

   /// Returns the set of elements contained in `self` or in `other`,
   /// but not in both `self` and `other`.
   @warn_unused_result
-  func exclusiveOr(other: Self) -> Self
+  func exclusiveOring(with other: Self) -> Self

   /// If `member` is not already contained in `self`, inserts it.
   ///
@@ -90,53 +90,53 @@ public protocol SetAlgebra : Equatable, ArrayLiteralConvertible {
   /// Insert all elements of `other` into `self`.
   ///
   /// - Equivalent to replacing `self` with `self.union(other)`.
-  /// - Postcondition: `self.isSupersetOf(other)`
-  mutating func unionInPlace(other: Self)
+  /// - Postcondition: `self.isSuperset(of other)`
+  mutating func union(with other: Self)

   /// Removes all elements of `self` that are not also present in
   /// `other`.
   ///
   /// - Equivalent to replacing `self` with `self.intersect(other)`
-  /// - Postcondition: `self.isSubsetOf(other)`
-  mutating func intersectInPlace(other: Self)
+  /// - Postcondition: `self.isSubset(of other)`
+  mutating func intersect(with other: Self)

   /// Replaces `self` with a set containing all elements contained in
   /// either `self` or `other`, but not both.
   ///
   /// - Equivalent to replacing `self` with `self.exclusiveOr(other)`
-  mutating func exclusiveOrInPlace(other: Self)
+  mutating func exclusiveOr(with other: Self)

   //===--- Requirements with default implementations ----------------------===//
   /// Returns the set of elements contained in `self` but not in `other`.
   @warn_unused_result
-  func subtract(other: Self) -> Self
+  func subtracting(other: Self) -> Self

   /// Return true iff every element of `self` is contained in `other`.
   @warn_unused_result
-  func isSubsetOf(other: Self) -> Bool
+  func isSubset(of other: Self) -> Bool

   /// Return true iff `self.intersect(other).isEmpty`.
   @warn_unused_result
-  func isDisjointWith(other: Self) -> Bool
+  func isDisjoint(with other: Self) -> Bool

   /// Return true iff every element of `other` is contained in `self`.
   @warn_unused_result
-  func isSupersetOf(other: Self) -> Bool
+  func isSuperset(of other: Self) -> Bool

   /// Return true iff `self.contains(e)` is `false` for all `e`.
   var isEmpty: Bool { get }

   /// Creates the set containing all elements of `sequence`.
-  init<S : Sequence where S.Iterator.Element == Element>(_ sequence: S)
+  init<S : SequenceType where S.Generator.Element == Element>(_ sequence: S)

   /// Removes all elements of `other` from `self`.
   ///
   /// - Equivalent to replacing `self` with `self.subtract(other)`.
-  mutating func subtractInPlace(other: Self)
+  mutating func subtract(other: Self)

   /// Returns `true` iff `a` subsumes `b`.
   ///
-  /// - Equivalent to `([a] as Self).isSupersetOf([b])`
+  /// - Equivalent to `([a] as Self).isSuperset(of: [b])`
   @warn_unused_result
   static func element(a: Element, subsumes b: Element) -> Bool

@@ -182,13 +182,13 @@ extension SetAlgebra {

   /// Returns true iff every element of `self` is contained in `other`.
   @warn_unused_result
-  public func isSubsetOf(other: Self) -> Bool {
+  public func isSubset(of other: Self) -> Bool {
     return self.intersect(other) == self
   }

   /// Returns true iff every element of `other` is contained in `self`.
   @warn_unused_result
-  public func isSupersetOf(other: Self) -> Bool {
+  public func isSuperset(of other: Self) -> Bool {
     return other.isSubsetOf(self)
   }

@@ -212,20 +212,20 @@ extension SetAlgebra {
   /// Returns true iff every element of `other` is contained in `self`
   /// and `self` contains an element that is not contained in `other`.
   @warn_unused_result
-  public func isStrictSupersetOf(other: Self) -> Bool {
+  public func isStrictSuperset(of other: Self) -> Bool {
     return self.isSupersetOf(other) && self != other
   }

   /// Return true iff every element of `self` is contained in `other`
   /// and `other` contains an element that is not contained in `self`.
   @warn_unused_result
-  public func isStrictSubsetOf(other: Self) -> Bool {
+  public func isStrictSubset(of other: Self) -> Bool {
     return other.isStrictSupersetOf(self)
   }

   /// Returns `true` iff `a` subsumes `b`.
   ///
-  /// - Equivalent to `([a] as Self).isSupersetOf([b])`
+  /// - Equivalent to `([a] as Self).isSuperset(of: [b])`
   @warn_unused_result
   public static func element(a: Element, subsumes b: Element) -> Bool {
     return ([a] as Self).isSupersetOf([b])