diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index b9facb8..ec2ded0 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -34,9 +34,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 5.pdf",
-                "page": 4,
+                "page": 6,
                 "left": -27,
-                "top": 131,
+                "top": 172,
                 "zoom": 0.5754156769596199
               },
               "icon": "lucide-file-text",
@@ -218,9 +218,10 @@
   },
   "active": "6edd4157a160e462",
   "lastOpenFiles": [
-    "Concurrent Systems/notes/4c - Dining Philosophers.md",
-    "Concurrent Systems/notes/5 - Software Transactional Memory.md",
+    "Concurrent Systems/notes/images/Pasted image 20250317105355.png",
     "Concurrent Systems/slides/class 5.pdf",
+    "Concurrent Systems/notes/5 - Software Transactional Memory.md",
+    "Concurrent Systems/notes/4c - Dining Philosophers.md",
     "Concurrent Systems/slides/class 4.pdf",
     "Concurrent Systems/notes/images/Pasted image 20250317100456.png",
     "Concurrent Systems/notes/4b - Monitors.md",
diff --git a/Concurrent Systems/notes/5 - Software Transactional Memory.md b/Concurrent Systems/notes/5 - Software Transactional Memory.md
index 9eb3feb..4948621 100644
--- a/Concurrent Systems/notes/5 - Software Transactional Memory.md	
+++ b/Concurrent Systems/notes/5 - Software Transactional Memory.md	
@@ -57,3 +57,19 @@ We now present an atomic STM system, called *Transactional Locking 2*:
 ```
 poi la scrivo giuro
 ```
+
+### Virtual World Consistency
+Opacity requires a total order on all committed transactions and on all read prefixes of all aborted transactions
+	this latter requirement can be weakened by imposing that the read prefix of an aborted transaction is consistent only w.r.t its casual past (i.e. its virtual world).
+
+**Opacity:** total order both on all committed transactions and on read prefixes of aborted transactions
+
+**VWC:** total order on all committed transactions + partial order on committed transactions and the read prefixes of aborted transactions.
+
+The **casual past** of a transaction T is the set of all T' and T'' such that
+- T reads a value written by T'
+- T'' belongs to the casual past of T'
+
+VWC allows more transactions to commit -> it is a more liberal property than opacity.
+
+![[Pasted image 20250317105355.png]]
diff --git a/Concurrent Systems/notes/images/Pasted image 20250317105355.png b/Concurrent Systems/notes/images/Pasted image 20250317105355.png
new file mode 100644
index 0000000..ad5ea63
Binary files /dev/null and b/Concurrent Systems/notes/images/Pasted image 20250317105355.png differ