What types of beer have lower or no carbonation?
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What you will be looking for is a Cask ale or cask-conditioned beer these are all generally very low carbonation or non at all due to only being left in a cask
"Beer brewed from traditional ingredients, matured by secondary fermentation in the container from which it is dispensed, and served without the use of extraneous carbon dioxide"
If you go to an ale bar they will usually have at least one cask ale on I have not done a tour of America, so I cannot for sure tell you of places in America for low carbonated beer, but as for the what type of beer Cask Conditioned is definitely what you should be looking for.