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people who understand latin grammar, how would I make a phrase like pax romana but with ludo (play) in place of roma? pax ludens? pax ludica?
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Depends on what you want to convey. 'romana' is an adjective (feminine singular inflection of romanus; Roman) while ludo is a verb meaning 'I play'. 'ludi' is genitive singular of ludus (game), so the literal meaning of 'pax ludi' would be 'peace of [the] game'.
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Romanus is an adjective -- "roman peace" not "peace of the romans" So pax ludi or pax ludorum = "peace of the game(s)" For adjective form, could go with ludicra (!) which per the dictionary= "connected with sport or the stage"
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