diff --git a/tests/test_option_setting.py b/tests/test_option_setting.py
index fef7d1c..9cc3323 100644
--- a/tests/test_option_setting.py
+++ b/tests/test_option_setting.py
@@ -76,14 +76,13 @@ def test_mod_read_only_write():
                                                                   'mandatory',
                                                                   'empty'}
     #
-    config.property.setdefault({'cache'})
-    config.property.setdefault(type='read_only', when='append', properties={'disabled'})
-    config.property.setdefault(type='read_only', when='remove', properties={'hidden'})
-    config.property.setdefault(type='read_write', when='append', properties={'disabled',
-                                                                             'hidden'})
-    config.property.setdefault(type='read_write', when='remove', properties=set([]))
-    raises(ValueError, "config.property.setdefault(type='unknown', when='append', properties={'disabled'})")
-    raises(ValueError, "config.property.setdefault(type='read_only', when='unknown', properties={'disabled'})")
+    config.property.setdefault(frozenset(['cache']))
+    config.property.setdefault(type='read_only', when='append', properties=frozenset(['disabled']))
+    config.property.setdefault(type='read_only', when='remove', properties=frozenset(['hidden']))
+    config.property.setdefault(type='read_write', when='append', properties=frozenset(['disabled', 'hidden']))
+    config.property.setdefault(type='read_write', when='remove', properties=frozenset([]))
+    raises(ValueError, "config.property.setdefault(type='unknown', when='append', properties=frozenset(['disabled']))")
+    raises(ValueError, "config.property.setdefault(type='read_only', when='unknown', properties=frozenset(['disabled']))")
     raises(TypeError, "config.property.setdefault(type='read_only', when='append', properties=['disabled'])")
 
     assert config.property.getdefault() == {'cache'}
diff --git a/tiramisu/api.py b/tiramisu/api.py
index 16ed2ed..fa9b030 100644
--- a/tiramisu/api.py
+++ b/tiramisu/api.py
@@ -1047,8 +1047,8 @@ class TiramisuContextProperty(TiramisuContext):
                    properties: Set[str],
                    type: Optional[str]=None,
                    when: Optional[str]=None) -> None:
-        if not isinstance(properties, set):
-            raise TypeError(_('properties must be a set'))
+        if not isinstance(properties, frozenset):
+            raise TypeError(_('properties must be a frozenset'))
         setting = self._config_bag.context.cfgimpl_get_settings()
         if type is None and when is None:
             setting.default_properties = properties
diff --git a/tiramisu/config.py b/tiramisu/config.py
index d399376..c9bdd30 100644
--- a/tiramisu/config.py
+++ b/tiramisu/config.py
@@ -688,6 +688,11 @@ class _CommonConfig(SubConfig):
         duplicated_config.cfgimpl_get_settings()._p_.importation(properties)
         duplicated_config.cfgimpl_get_settings()._pp_.importation(self.cfgimpl_get_settings(
             )._pp_.exportation())
+        duplicated_config.cfgimpl_get_settings().ro_append = self.cfgimpl_get_settings().ro_append
+        duplicated_config.cfgimpl_get_settings().rw_append = self.cfgimpl_get_settings().rw_append
+        duplicated_config.cfgimpl_get_settings().ro_remove = self.cfgimpl_get_settings().ro_remove
+        duplicated_config.cfgimpl_get_settings().rw_remove = self.cfgimpl_get_settings().rw_remove
+        duplicated_config.cfgimpl_get_settings().default_properties = self.cfgimpl_get_settings().default_properties
         duplicated_config.cfgimpl_reset_cache(None, None)
         if child is not None:
             duplicated_config._impl_children.append(child)
@@ -1269,6 +1274,11 @@ class KernelMetaConfig(KernelMixConfig):
         if new:
             config.cfgimpl_get_settings().set_context_properties(self.cfgimpl_get_settings().get_context_properties(), config)
             config.cfgimpl_get_settings().set_context_permissives(self.cfgimpl_get_settings().get_context_permissives())
+            config.cfgimpl_get_settings().ro_append = self.cfgimpl_get_settings().ro_append
+            config.cfgimpl_get_settings().rw_append = self.cfgimpl_get_settings().rw_append
+            config.cfgimpl_get_settings().ro_remove = self.cfgimpl_get_settings().ro_remove
+            config.cfgimpl_get_settings().rw_remove = self.cfgimpl_get_settings().rw_remove
+            config.cfgimpl_get_settings().default_properties = self.cfgimpl_get_settings().default_properties
 
         config._impl_meta = weakref.ref(self)
         self._impl_children.append(config)