I found this in my notes. Sin = lawlessness. World =
41.38 κόσμοςc, ου m; αἰώνc, ῶνος m: the system of practices and standards associated with secular society (that is, without reference to any demands or requirements of God)—‘world system, world’s standards, world.’
Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains (electronic ed. of the 2nd edition., Vol. 1, p. 507). New York: United Bible Societies.
TDNT Entry
an apt and harmonious arrangement or constitution, order, government
ornament, decoration, adornment, i.e. the arrangement of the stars, 'the heavenly hosts', as the ornament of the heavens. 1 Pet. 3:
the world, the universe
the circle of the earth, the earth
the inhabitants of the earth, men, the human family
the ungodly multitude; the whole mass of men alienated from God, and therefore hostile to the cause of Christ
world affairs, the aggregate of things earthly
the whole circle of earthly goods, endowments riches, advantages, pleasures, etc, which although hollow and frail and fleeting, stir desire, seduce from God and are obstacles to the cause of Christ
any aggregate or general collection of particulars of any sort
the Gentiles as contrasted to the Jews (Rom. 11:12 etc)
of believers only, John 1:29; 3:16; 3:17; 6:33; 12:47 1 Cor. 4:9; 2 Cor. 5:19
2. When what is constructed consists of people, we find the sense of “human order,” e.g., of rowers, of an army, or of a city or state.
Kittel, G., Friedrich, G., & Bromiley, G. W. (1985). Theological Dictionary of the New Testament (p. 460). Grand Rapids, MI: W.B. Eerdmans.
So I would think Jesus accomplishes this in the saved world of the New Heavens and earth.