Mt’s Judgment expressions imply Q. E.g. here's the NT ‘Judgement Day’ Expressions (not including "on that day"):

1 Jn 4:17 "at the day of the judgment" en th ‘hmera ths krisews

2 Pt 2:4 "unto [the] judgment" eis krisin

2 Pt 2:9 & 3:7 "unto day of-judgment" eis ‘hmeran krisews

Jd 1:6 "unto mega judgment day" eis krisin megalhs ‘hmeras

Hb 9:17 "[the] judgment" krisis

Lk 10:14, 11:31 & 32 (cf. Mt 12:41,42)"at the judgment" en th krisei

Mt 10:15; 11:22 , 24; 12:36 "at day of-judgment" en ‘hmera krisews

It seems safe to say that Mt's "on Judgment Day" (en ‘hmera krisews) is Matthean. The expression is unique to Mt. Mt uses this expression four times (Mt 10:15; 11:22 , 24; 12:36).

Mt also shares with Lk the expression "at the judgment" en th krisei twice in the final two occurrences (in Mt 12:41, 42).

It could be argued that it is Luke who (in 11:31-32) adopts Mt’s EN TH KRISEI (from Mt 12:41-42). But Lk had already preferred the expression (in Lk 10:14) when he supposedly already changed Mt’s preferred expression ("at Judgment Day" Mt 11:22) to "at the judgment." Farrer theorists might argue that Lk simply prefers his own expression to Mt’s and so is consistent in changing it. But the theory cannot account for Mt’s behaviour. Why is Mt inconsistent when he seems to prefer the expression he used four times (esp. Mt 12:36). Thus my problem with the Farrer theory is that it cannot explain Mt’s behaviour here since Lk’s presence should have no affect.

Thus it seems that editorial fatigue better explains Mt’s alternation between his two different expressions. Mt’s preferred expression is the one found in 12:36 (no Lk parallels) en ‘hmera krisews ("at/on Judgment Day") and he slips into reproducing his source’s expression in 12:41-42 "at the judgment" (from his oral or written "Q" source). The Mark-Q theory can explain both Mt’s and Lk’s expressions whilst the Farrer (Mk-Mt) theory leaves unexplained why the expression in Lk differs to Mt’s preferred expression but coincides with Mt’s final two.

Mt’s use of Lk could also explain the phenomena but Lk’s use of Mt cannot fully explain it.

Tim Lewis.