You well know the benefits of fermented vegetables: lactobacilli they contain enhance their digestibility and increases vitamin levels. These beneficial organisms produce numerous helpful enzymes as well as antibiotic and anticarcinogenic substances. Besides they decrease carbohydrate amount.

I often lacto-ferment vegetables (white and red cabbage, cucumbers, carrots, radish, garlic), below e.g. is one of my preferred ways to ferment white cabbage:

Fermented cabbage in Peter the Great’s style
87 oz. white cabbage
2 carrots
2 large onion heads
2 garlic cloves
2 tbsp olive oil
2.5 tbsp salt
3.5 oz vinegar
2 pcs. sucralose (or other sweetener)

1. For pickle solution boil 1L water with salt and sweetener.
2. Shred the cabbage, grate carrot, onion – in half rings, mince garlic cloves.
3. Stir all the ingredients, put in a jar or a pot, and pour into olive oil, vinegar and hot pickle solution.
4. Put press on top (I use another jar filed with water), place into fridge. Due in 3 days (to tell the truth, my relatives start to steal cabbage already the next day).

Comment: May skip or reduce sweetener if prefer sour taste. (though then it’s not the Peter’s)

Sounds like Kimchee!!! Instead of putting it in the fridge, bury it for a week- thats how mom used to do it!

How can it ferment in the fridge? Usually things have to be left out at room temperature... also the vinegar would kill the bacteria too. Are you sure you're not just eating pickled cabbage?