diff --git a/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.compile.pass.cpp b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.compile.pass.cpp
new file mode 100644
index 0000000000..07dc03b431
--- /dev/null
+++ b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.compile.pass.cpp
@@ -0,0 +1,55 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+// SPDX-FileCopyrightText: Copyright (c) 2023 NVIDIA CORPORATION & AFFILIATES
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14
+
+// template<class I, class R = ranges::less, class P = identity>
+//   concept sortable = see below;                            // since C++20
+
+#include <cuda/std/iterator>
+
+#include <cuda/std/functional>
+
+using CompInt = bool(*)(int, int);
+using CompDefault = cuda::std::ranges::less;
+
+using AllConstraintsSatisfied = int*;
+static_assert( cuda::std::permutable<AllConstraintsSatisfied>);
+static_assert( cuda::std::indirect_strict_weak_order<CompDefault, AllConstraintsSatisfied>);
+static_assert( cuda::std::sortable<AllConstraintsSatisfied>);
+static_assert( cuda::std::indirect_strict_weak_order<CompInt, AllConstraintsSatisfied>);
+static_assert( cuda::std::sortable<AllConstraintsSatisfied, CompInt>);
+
+struct Foo {};
+using Proj = int(*)(Foo);
+static_assert( cuda::std::permutable<Foo*>);
+static_assert(!cuda::std::indirect_strict_weak_order<CompDefault, Foo*>);
+static_assert( cuda::std::indirect_strict_weak_order<CompDefault, cuda::std::projected<Foo*, Proj>>);
+static_assert(!cuda::std::sortable<Foo*, CompDefault>);
+static_assert( cuda::std::sortable<Foo*, CompDefault, Proj>);
+static_assert(!cuda::std::indirect_strict_weak_order<CompInt, Foo*>);
+static_assert( cuda::std::indirect_strict_weak_order<CompInt, cuda::std::projected<Foo*, Proj>>);
+static_assert(!cuda::std::sortable<Foo*, CompInt>);
+static_assert( cuda::std::sortable<Foo*, CompInt, Proj>);
+
+using NotPermutable = const int*;
+static_assert(!cuda::std::permutable<NotPermutable>);
+static_assert( cuda::std::indirect_strict_weak_order<CompInt, NotPermutable>);
+static_assert(!cuda::std::sortable<NotPermutable, CompInt>);
+
+struct Empty {};
+using NoIndirectStrictWeakOrder = Empty*;
+static_assert( cuda::std::permutable<NoIndirectStrictWeakOrder>);
+static_assert(!cuda::std::indirect_strict_weak_order<CompInt, NoIndirectStrictWeakOrder>);
+static_assert(!cuda::std::sortable<NoIndirectStrictWeakOrder, CompInt>);
+
+int main(int, char**)
+{
+  return 0;
+}
diff --git a/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.subsumption.compile.pass.cpp b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.subsumption.compile.pass.cpp
new file mode 100644
index 0000000000..ec6c662a97
--- /dev/null
+++ b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.subsumption.compile.pass.cpp
@@ -0,0 +1,33 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+// SPDX-FileCopyrightText: Copyright (c) 2023 NVIDIA CORPORATION & AFFILIATES
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+
+// template<class I, class R = ranges::less, class P = identity>
+//   concept sortable = see below;                            // since C++20
+
+#include <cuda/std/iterator>
+
+#include <cuda/std/functional>
+
+template <class I, class R, class P>
+__host__ __device__ void test_subsumption() requires cuda::std::permutable<I>;
+
+template <class I, class R, class P>
+__host__ __device__ void test_subsumption() requires cuda::std::indirect_strict_weak_order<R, cuda::std::projected<I, P>>;
+
+template <class I, class R, class P>
+__host__ __device__ constexpr bool test_subsumption() requires cuda::std::sortable<I, R, P> { return true; }
+
+static_assert(test_subsumption<int*, cuda::std::ranges::less, cuda::std::identity>());
+
+int main(int, char**)
+{
+  return 0;
+}
diff --git a/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt b/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt
index d31e72704f..a198ffe7a4 100644
--- a/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt
+++ b/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt
@@ -109,6 +109,7 @@ set(files
   __iterator/reverse_access.h
   __iterator/reverse_iterator.h
   __iterator/size.h
+  __iterator/sortable.h
   __iterator/wrap_iter.h
   __libcpp_version
   __locale
diff --git a/libcudacxx/include/cuda/std/detail/libcxx/include/__iterator/sortable.h b/libcudacxx/include/cuda/std/detail/libcxx/include/__iterator/sortable.h
new file mode 100644
index 0000000000..17966f1cc3
--- /dev/null
+++ b/libcudacxx/include/cuda/std/detail/libcxx/include/__iterator/sortable.h
@@ -0,0 +1,53 @@
+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+// SPDX-FileCopyrightText: Copyright (c) 2023 NVIDIA CORPORATION & AFFILIATES
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCUDACXX___ITERATOR_SORTABLE_H
+#define _LIBCUDACXX___ITERATOR_SORTABLE_H
+
+#ifndef __cuda_std__
+#include <__config>
+#endif // __cuda_std__
+
+#include "../__functional/identity.h"
+#include "../__functional/ranges_operations.h"
+#include "../__iterator/concepts.h"
+#include "../__iterator/permutable.h"
+#include "../__iterator/projected.h"
+
+#if defined(_LIBCUDACXX_USE_PRAGMA_GCC_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCUDACXX_BEGIN_NAMESPACE_STD
+
+#if _LIBCUDACXX_STD_VER > 17
+
+template <class _Iter, class _Comp = _CUDA_VRANGES::less, class _Proj = identity>
+concept sortable =
+  permutable<_Iter> &&
+  indirect_strict_weak_order<_Comp, projected<_Iter, _Proj>>;
+
+#elif _LIBCUDACXX_STD_VER > 14
+
+template <class _Iter, class _Comp, class _Proj>
+_LIBCUDACXX_CONCEPT_FRAGMENT(
+  __sortable_,
+  requires() //
+  (requires(permutable<_Iter>),
+   requires(indirect_strict_weak_order<_Comp, projected<_Iter, _Proj>>)));
+
+template <class _Iter, class _Comp = _CUDA_VRANGES::less, class _Proj = identity>
+_LIBCUDACXX_CONCEPT sortable = _LIBCUDACXX_FRAGMENT(__sortable_, _Iter, _Comp, _Proj);
+
+#endif // _LIBCUDACXX_STD_VER > 14
+
+_LIBCUDACXX_END_NAMESPACE_STD
+
+#endif // _LIBCUDACXX___ITERATOR_SORTABLE_H
diff --git a/libcudacxx/include/cuda/std/detail/libcxx/include/iterator b/libcudacxx/include/cuda/std/detail/libcxx/include/iterator
index 5ebd60d861..fb026ab91f 100644
--- a/libcudacxx/include/cuda/std/detail/libcxx/include/iterator
+++ b/libcudacxx/include/cuda/std/detail/libcxx/include/iterator
@@ -710,6 +710,7 @@ template <class E> constexpr const E* data(initializer_list<E> il) noexcept;
 #include "__iterator/reverse_access.h"
 #include "__iterator/reverse_iterator.h"
 #include "__iterator/size.h"
+#include "__iterator/sortable.h"
 #include "__iterator/wrap_iter.h"
 #include "__memory/addressof.h"
 #include "__memory/pointer_traits.h"
diff --git a/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.compile.pass.cpp b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.compile.pass.cpp
new file mode 100644
index 0000000000..2a2c828500
--- /dev/null
+++ b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.compile.pass.cpp
@@ -0,0 +1,53 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+
+// template<class I, class R = ranges::less, class P = identity>
+//   concept sortable = see below;                            // since C++20
+
+#include <iterator>
+
+#include <functional>
+
+using CompInt = bool(*)(int, int);
+using CompDefault = std::ranges::less;
+
+using AllConstraintsSatisfied = int*;
+static_assert( std::permutable<AllConstraintsSatisfied>);
+static_assert( std::indirect_strict_weak_order<CompDefault, AllConstraintsSatisfied>);
+static_assert( std::sortable<AllConstraintsSatisfied>);
+static_assert( std::indirect_strict_weak_order<CompInt, AllConstraintsSatisfied>);
+static_assert( std::sortable<AllConstraintsSatisfied, CompInt>);
+
+struct Foo {};
+using Proj = int(*)(Foo);
+static_assert( std::permutable<Foo*>);
+static_assert(!std::indirect_strict_weak_order<CompDefault, Foo*>);
+static_assert( std::indirect_strict_weak_order<CompDefault, std::projected<Foo*, Proj>>);
+static_assert(!std::sortable<Foo*, CompDefault>);
+static_assert( std::sortable<Foo*, CompDefault, Proj>);
+static_assert(!std::indirect_strict_weak_order<CompInt, Foo*>);
+static_assert( std::indirect_strict_weak_order<CompInt, std::projected<Foo*, Proj>>);
+static_assert(!std::sortable<Foo*, CompInt>);
+static_assert( std::sortable<Foo*, CompInt, Proj>);
+
+using NotPermutable = const int*;
+static_assert(!std::permutable<NotPermutable>);
+static_assert( std::indirect_strict_weak_order<CompInt, NotPermutable>);
+static_assert(!std::sortable<NotPermutable, CompInt>);
+
+struct Empty {};
+using NoIndirectStrictWeakOrder = Empty*;
+static_assert( std::permutable<NoIndirectStrictWeakOrder>);
+static_assert(!std::indirect_strict_weak_order<CompInt, NoIndirectStrictWeakOrder>);
+static_assert(!std::sortable<NoIndirectStrictWeakOrder, CompInt>);
+
+int main(int, char**) {
+  return 0;
+}
diff --git a/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.subsumption.compile.pass.cpp b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.subsumption.compile.pass.cpp
new file mode 100644
index 0000000000..8cd5e48d89
--- /dev/null
+++ b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.sortable/sortable.subsumption.compile.pass.cpp
@@ -0,0 +1,29 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+
+// template<class I, class R = ranges::less, class P = identity>
+//   concept sortable = see below;                            // since C++20
+
+#include <iterator>
+
+#include <functional>
+
+template <class I, class R, class P> void test_subsumption() requires std::permutable<I>;
+
+template <class I, class R, class P> void test_subsumption()
+    requires std::indirect_strict_weak_order<R, std::projected<I, P>>;
+
+template <class I, class R, class P> constexpr bool test_subsumption() requires std::sortable<I, R, P> { return true; }
+
+static_assert(test_subsumption<int*, std::ranges::less, std::identity>());
+
+int main(int, char**) {
+  return 0;
+}