diff --git a/loopy/kernel.py b/loopy/kernel.py
index 6fea7bfaca4b3dba748b6a292b64badfc39642a2..d8d78ece8ce38e8f921cfbe61af27c62b41dc104 100644
--- a/loopy/kernel.py
+++ b/loopy/kernel.py
@@ -960,7 +960,7 @@ class LoopKernel(Record):
         result = set()
         for dom in self.domains:
             result.update(dom.get_var_names(dim_type.set))
-        return result
+        return frozenset(result)
 
     @memoize_method
     def non_iname_variable_names(self):