diff --git a/python/egglog/egraph_state.py b/python/egglog/egraph_state.py
index 876466e1..726a681b 100644
--- a/python/egglog/egraph_state.py
+++ b/python/egglog/egraph_state.py
@@ -858,8 +858,12 @@ def _exprs_multiple_parents(typed_expr: TypedExprDecl) -> list[TypedExprDecl]:
     """
     Returns all expressions that have multiple parents (a list but semantically just an ordered set).
     """
-    to_traverse = {typed_expr}
-    traversed = set[TypedExprDecl]()
+    # Traverse with a deterministic LIFO worklist instead of a set of objects:
+    # popping from a set iterates in id()-hash order (memory addresses), which
+    # varies per process and made the hoisting order (and hence the $__expr_N
+    # let numbering and e-class ids) nondeterministic across runs.
+    to_traverse = [typed_expr]
+    traversed: set[TypedExprDecl] = set()
     traversed_twice = list[TypedExprDecl]()
     while to_traverse:
         typed_expr = to_traverse.pop()
@@ -869,9 +873,9 @@ def _exprs_multiple_parents(typed_expr: TypedExprDecl) -> list[TypedExprDecl]:
         traversed.add(typed_expr)
         expr = typed_expr.expr
         if isinstance(expr, CallDecl):
-            to_traverse.update(expr.args)
+            to_traverse.extend(expr.args)
         elif isinstance(expr, PartialCallDecl):
-            to_traverse.update(expr.call.args)
+            to_traverse.extend(expr.call.args)
     return traversed_twice
 
 
diff --git a/python/tests/test_deterministic_hoisting.py b/python/tests/test_deterministic_hoisting.py
new file mode 100644
index 00000000..42e62aab
--- /dev/null
+++ b/python/tests/test_deterministic_hoisting.py
@@ -0,0 +1,56 @@
+"""
+Expression hoisting must be deterministic across processes.
+
+`_exprs_multiple_parents` used to traverse the expression DAG with a set of
+``TypedExprDecl`` objects and ``.pop()`` from it, so the traversal order --
+and with it the order in which shared subterms were hoisted into
+``$__expr_N`` let-bindings -- depended on id()-based hashing (memory
+addresses).  Identical programs were therefore lowered into different
+(equivalent) e-graphs in different processes, making ``serialize()`` output
+nondeterministic.
+"""
+
+import subprocess
+import sys
+
+SCRIPT = """
+from __future__ import annotations
+
+import hashlib
+
+from egglog import EGraph, Expr, StringLike
+
+
+class B(Expr):
+    @classmethod
+    def var(cls, name: StringLike) -> B: ...
+
+    def __and__(self, o: B) -> B: ...
+
+    def __or__(self, o: B) -> B: ...
+
+    def __invert__(self) -> B: ...
+
+
+eg = EGraph()
+x, y = B.var("x"), B.var("y")
+shared = x & y
+expr = shared | y
+for _ in range(24):
+    expr = (shared & expr) | (expr & (shared | x))
+eg.let("$e", expr)
+print(hashlib.sha256(eg._serialize().to_json().encode()).hexdigest())
+"""
+
+
+def test_serialization_is_deterministic_across_processes() -> None:
+    hashes = []
+    for _ in range(3):
+        proc = subprocess.run(
+            [sys.executable, "-c", SCRIPT],
+            capture_output=True,
+            text=True,
+            check=True,
+        )
+        hashes.append(proc.stdout.strip())
+    assert len(set(hashes)) == 1, f"nondeterministic serialization: {hashes}"