oil-based for kitchens is most recommended.... de-grease with TSP or a mixture of Dawn for dishes and water, then lightly sand, wipe clean and apply paint. oil-based for primer and paint....
of course, i could be wrong now..... but i don't think so.....
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If you are going to paint white than I would use a water based topcoat like ben moores waterborne Satin Impervo, or Cabinet Coat, or a similar product. White Oil based paints will turn yellow, especially in a kitchen over time. The water based whites will stay a brighter white. Most of the times you don't even realize they are yellowing, however if you have white appliances they stick out like a sore thumb. Ditto the previous comments on cleaning and priming first - can't go wrong with an oil based primer - could get away with using 1-2-3 or a similar bonding primer.