For sauerkraut you don't even need a fancy jar. I use a big old coffee jar. I cut a cabbage leaf to fit over the top of the shredded cabbage so none floats up. I weigh that down with an old spice jar. The cabbage stays under the surface of the brine so the environment is naturally anaerobic.
it's easier than that. Take small cabbage heads (also works if cut into pieces, salad style). Put in some container - plastic tank, wooden barrel, glass jar, whatever - 2-or-20-or-120 liters. Add (sea) salt - 30-50g-per-liter-of-water (handwavey, can be corrected later), some grains of corn (or whole cob), a piece of apple, maybe some ginger, fill with water to cover the ingredients.. add something on top to keep things down, like river stone or heavy dish. Keep at below 15'C without freezeing (here usually in November, outside in the balcony.. until March). Once in a while have the water go up-down-up - which i do by just quickly kicking the jar for a minute.
Best eaten as salad with oil and red-pepper, and of course, wrapping pork minceballs.
nazdrave
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