A person once sent me a private email in which he questioned the idea of Christian teaching being dictated (governed) by a select group of men in a central location. Part of his argument was based on Acts 16:4 which uses the Greek expression τὰ δόγματα.
The apostles and older men at Jerusalem constituted an authoritative body of men who governed early believers and made important decisions regarding matters of doctrine, faith and morals. According to Acts 2:42, early Christians (after Pentecost) obeyed apostolic teaching; the preeminence of the apostles is likewise suggested by the vision that John received of New Jerusalem in Revelation 21. That account depicts the apostles as foundation stones of the holy city.
In order to make a proper determination about what τὰ δόγματα may denote, we need to have more up to date resources than Strong's Concordance or Thayer's Greek-English lexicon since these publications do not include the contemporary work done after the Greek papyri of Egypt were discovered: knowledge of the Greek language has advanced since the publication of Strong or Thayer.
Granted, the term "dogma" evidently does not have the force of an imperial command in Acts 16:4 as one finds in Luke 2:1. Rather, the more probable meaning in Acts 16:4 is "a formal statement concerning rules or regulations that are to be observed" (BDAG Greek-English Lexicon, 254) Compare Ephesians 2:15; Colossians 2:14.
Every Greek text that I own (including UBS4 and NA27) has the reading τὰ δόγματα in the main text. τὰ δόγματα further seems to be attested in the homilies (Acts of the Apostles) of John Chrysostom. [Compare the new NA28 as well.]
I see no good reason to eschew the reading τὰ δόγματα in view of what we find in ancient writers and modern Greek texts. For a useful diachronic approach to the Greek term "dogma", see Theological Dictionary of the New Testament, volume 2:231-232. This source demonstrates that a number of early Christian writers understood "dogma" as a term that could be applied to "the teachings and prescriptions of Jesus." TDNT itself describes the word (within the context of Acts 16:4) as referring to "the resolutions and decrees of the early church in Jerusalem which are to be sent out to the cities of the first missionary journey" (ibid). Even if the word is used to describe philosophical notions or imperial edicts in antiquity, TDNT suggests that "dogma" appears to reference divine law in Acts 16:4.
The apostles and older men mentioned in Acts 15 and 16 were dealing with a certain problem, namely, circumcision and its relation to soteriology (the doctrine of salvation). There was no need to impose further burdens at that time on the Gentiles. While some who oppose the structure discussed in Acts want to imply that the apostolic model may be too confining or restrictive, I do not believe that "all powerful" is the right way to view the "Governing Body" that resided in first century Jerusalem--nor is that how I view today's Governing Body of Jehovah's Witnesses.
The apostles and older men were servants of God who endeavored to provide guidance for the budding first century congregations: they exercised due humility and modesty while relying upon the Most High God, Jehovah. Their official functions in setting forth "dogma" must be viewed in the light of Acts 20:28ff; Hebrews 13:7, 17; 1 Peter 5:1-5.