Verheyden, Joseph. "Chapter Six: Jewish Christianity, A State of Affairs: Affinities and Differences with Respect to Matthew, James, and the Didache." in Van de Sandt, Huub & Zangenberg, Jürgen K. (editors). Matthew, James, and Didache: Three Related Documents in their Jewish and Christian Settings." Atlanta, GA: Society of Biblical Literature, 2008, 123-135.
Verheyden takes Matthew, James, and the Didache all to be written by authors of Jewish descent. He considers, then, that making a definition of "Jewish Christianity" is important (Verheyden 2008, 123).
One of the primary difficulties in defining Jewish Christianity is interpreting archaeological remains, including inscriptions. Scholars disagree as to the actual nature of communities (Verheyden 2008, 124). Verheyden asserts that we are certainly unable to identify the specific communities from which Matthew, James, and the Didache arose, a fact which complicates archaeological analysis.
Textual evidence is also challenging, as it is not always clear what may be genuine, especially among secondhand accounts. The Jewish Christians may have been considered heterodox by Church Fathers, so would often be ignored (Verheyden 2008, 125). Additionally, Matthew's Gospel was more widely embraced and used among Gentiles than in groups which would be considered Jewish Christians. This may have been because it was considered insufficiently Jewish (Verheyden 2008, 126).
The criteria for defining Jewish Christianity are unclear. There are a variety of ways in which a Christian of Jewish heritage may wish to express that heritage (Verheyden 2008, 126). The definition of orthodoxy remains important in this regard as well. The role of Torah in the theology and practice of Christians is a key distinguishing mark among different communities (Verheyden 2008, 128). The phenomenon of Jewish Christianity is naturally diverse.
The identity markers in Matthew, James, and the Didache were investigated in detail in 2004 by Gunnar Garleff in a monograph (Verheyden 2008, 128-129). Verheyden summarizes markers identified by Garleff, all of which pertain to the way a community expresses its identity as distinct from other communities (Verheyden 2008, 129). Matthew, James, and the Didache can be analyzed in terms of these identity markers.
Verheyden notes first that the three documents all show clear differentiation from one another. Matthew has a polemical style which sets it apart (Verheyden 2008, 130). It likely reflects a community which is still forming its distinct identity. The separation is not a matter of controversy in the Didache, and in James it appears complete. Matthew is concerned with the "story," the Didache with "ritus," and James with "ethos" (three more of Garleff's markers) (Verheyden 2008, 131). The documents each evidence a different source of authority as well (Verheyden 2008, 132). This results in a difference in the organization of each community.
Verheyden concludes that the three communities, all classified as Jewish Christians, have clear distinctions (Verheyden 2008, 133). They would reasonably be assumed to develop along different lines in future generations.