Consistency in a transaction, as far as I can see, has no meaning at all, let alone a mathematical one. It appears to me that it was only added to turn AID into ACID so that things could pass the ACID test. Atomic, Isolated, and Durable all have meanings that are easy to explain. I have never seen a description, let alone a definition, of Consistency that did not boil down to anything other than a tautology - "It's consistent iff it's consistent."
Consistency in a transaction, as far as I can see, has no meaning at all, let alone a mathematical one. It appears to me that it was only added to turn AID into ACID so that things could pass the ACID test. Atomic, Isolated, and Durable all have meanings that are easy to explain. I have never seen a description, let alone a definition, of Consistency that did not boil down to anything other than a tautology - "It's consistent iff it's consistent."
Take it down enough layers of abstraction and you'll see your so-called synchronous process is asynchronous anyway.