How long will shredded carrots keep

It should last years. If the reduction contains just vinegar, reduced until thick. This yields a very acidic solution very high in sugar (partly caramelized, depending on how long it was cooked). Other than sugar and acetic acid, there are some polyphenols and other gunk, some aromatics, and a bit of water.

There are two primary ways that food spoils: decay by microorganisms and oxidation. Decay happens when things get stinky and slimy, such as meat that has been left in a warm place for a few days. Bacteria can live in a lot of habitats, but need fairly mild conditions to thrive. Oxidation occurs when unsaturated fats (and other substances) pick up rogue chemicals from the environment, and is often refereed to as 'rancid'. This process will occur whenever something that can oxidize is exposed to air, but tends to progress slowly.

In the case of a balsamic reduction, the high acid and sugar content will stop bacterial growth. Since the reduction also contains acid, anything that could have been oxidized has already oxidized. Therefore a balsamic reduction should last pretty much forever. You might want to seal it up to keep bugs from getting in it, but other than that, it should be stable for years.

Not all turkeys are the same, and personally, I would not risk letting an entire turkey go rancid in the refrigerator. There is so much you don't know about this turkey:

• How was it butchered? In particular, how long was it sitting on the block and was it packed immediately afterward or left sitting out for a long time?

• How quickly was it cooled down to "transporting" temperature after butchering?

• Was it transported immediately, or was it stored for a while before transport, and if so, what were those storage conditions?

• How specifically was it transported? What were the environmental conditions, aside from temperature? Was it exposed to air? Could it have picked up any other contaminants?

• Just how cold was the refrigerator at Trader Joe's? Are you sure that it's consistently that cold?

• What if the turkey was shifted around? For example, what if some other customer picked it up, tossed it in a shopping cart, then after an hour of shopping decided to put it back?

• How did she transport it? I'm guessing in a non-temperature-controlled trunk? How long was it in that condition/environment before finally making it into the fridge?

• Was the temperature in the fridge turned down as far as it can go long before putting the turkey in there? If not, how long might it have taken to get down to the desired temperature, especially with a massive slightly-warmed-up turkey in there?

• How cold does her refrigerator get? Is it a new refrigerator? Are you both certain that it gets as cold as the rep at TJ's is assuming? Have you actually stuck a thermometer in there to measure the environmental temperature around where the turkey would be stored?

I'm not expecting you to answer any of these; my point is just that there are so many variables, so many things that can go wrong, and the quoted 10-day storage period (as well as the sell-by date) is for storage under ideal conditions.

I've seen turkeys go rancid in the fridge after just 2 days. I've seen others take longer, but still far less than 10 days to go rancid. It's an incredibly frustrating and completely avoidable experience. Just put it in the freezer! She just needs to make sure she gives it a couple of days to thaw in the fridge, due to the size of the bird. A half-frozen turkey on Thanksgiving day is almost as useless as a rancid one.