The Tosefta is a Halakhic work which corresponds in structure almost exactly to the Mishnah, with the same divisions for sedarim ("orders") and masekhot ("tractates"). It is mainly written in Mishnaic Hebrew, with some Aramaic.
The Tosefta attributes laws that are anonymous in the Mishnah to named Tannaim. It also augments the Mishnah with additional glosses and discussions. The Tosefta as we have it today functions like a commentary on unquoted Mishnaic material. It offers additional aggadic and midrashic material, and it sometimes contradicts the Mishnah in the ruling of Halakha (Jewish law), or in declaring in whose name a law was given.
However, a more conservative party opposed the exclusion of the rest of tradition and produced the Tosefta to avoid the impression that the written Mishnah was equivalent to the entire oral Torah. The original intention was that the two texts would be viewed on equal standing, but the succinctness of the Mishnah and the power and influence of Yehuda Ha-Nassi made it more popular among most students of tradition. Alberdina Houtman, Mishnah and Tosefta: A Synoptic Comparison of the Tractates Berakhot , Mohr Siebeck, 1996 Ultimately, the state of the source material is such to allow divergent opinions to exist.
See (for example) Jacob Neusner, The Law of Agriculture in the Mishnah and the Tosefta , Brill, 2005, especially page 1531.
Source: Wikipedia > Tosefta
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