Finite identification with positive and with complete data Dick de Jongh, Ana Lucia Vargas Abstract: We study the differences between finite identifiability of re- cursive languages with positive and with complete data. In finite families the difference lies exactly in the fact that for positive identification the families need to be anti-chains, while in in the infinite case it is less sim- ple, being an anti-chain is no longer a sufficent condition. We also show that with complete data there are no maximal learnable families whereas with positive data there usually are, but there do exist positively identifi- able familes without a maximal positively identifiable extension. We also investigate a conjecture of ours, namely that each positively identifiable family has either finitely many or continuously many maximal noneffec- tively positively identifiable extensions. We verify this conjecture for the restricted case of families of equinumerous finite languages.