The simple answer is, if a magnet sticks convincingly to the bottom of the pan, it should work on an induction burner. The magnet should land with a thud and not seem to float when it sticks.
There are all kinds (zillions) of stainless steel alloys. The kind of stainless steel used on refrigerators and dishwashers is not likely to be 18/8 and can actually rust in some cases. Besides, people need their refrigerator magnets! When you talk about stainless steel, I automatically think 18/8 stainless steel, that is, 18% chromium and 8% nickel. That widely accepted definition of stainless will not work on induction. It doesn't have enough iron.
There is 18/0 stainless which will work with a magnet and there will therefore work on an induction burner. 18/0 assumes no nickel. Besides the chromium, nickel and iron, there is some carbon mixed in with the iron to make it steel. It gives the iron more strength and hardness.
I have many older versions of All-Clad Copper Core, several that AC no longer makes, which are presumably 18/8 (magnet does not stick) and thus will not work on induction. Some years ago, All-Clad quietly started "dumbing down" many of their pans so they would work on induction. As I understand things, there may be some technical reasons with the cladding that prevents a few items from being made induction compatible. They didn't make a lot of noise about their products no longer being made of 18/8 stainless. Probably because it (18/0) could be perceived as degrading the quality.
Basically what All-Clad did was keep the inside stainless steel layer as 18/8 but dropped down the outside layer to (presumably) 18/0. Aluminum or copper layers are also routinely used in the middle because they do a better job of dispersing heat than SS.
I just checked and at least for Copper Core, All-Clad does now state in a round about way that the interior surface is 18/8 while the outer surface is induction compatible...but they don't say it's 18/0.. All-Clad does not laser etch their pans as induction ready. At least not since I last bought one. I own pretty much all the Copper Core there is so I haven't had any need to buy any in a while. Maybe things have changed. I do not believe there is any industry standard identifier for induction ready/compatible.
So, get the vendor/manufacturer to verify, check the manufacturer's website or use the magnet.