That's called moving the goalposts. Now that you personally know how to trace the reasoning to see that my counterexample really was a counterexample, you'll o

That's called moving the goalposts. Now that you personally know how to trace the reasoning to see that my counterexample really was a counterexample, you'll only accept it as a counterexample if you see it in published research? This is something that I worked through myself back in grad school back in the last millennium. https://www.researchgate.net/scientific-contributions/Marcia-J-Groszek-7375828 https://www.researchgate.net/scientific-contributions/Marcia... gave me a number of leading hints, and confirmed my reasoning to me. In particular she was the one who commented, "A lot of people miss the importance of the fact that an axiom system proving that it proves something doesn't mean that it proves something." From her reactions at the time, I'm pretty sure she thought it was trivially obvious. And may well have known of prior research. So no, I don't have published research using this formulation. Nor is it reasonable for you to demand published research to verify something learned through oral communication decades ago, which should be obvious to anyone in the field. Doubly so given that my first description of the counterexample came with enough specific details that you SHOULD have been able to figure it out yourself. I not only told you what definition would create the problem. I also said why, and gave you an outline of the construction from which you could produce the proof!