I believe there's a switch in the game setup, under "Mechanics"... it records the log of all players in the game (meaning you'll get everything from the AI Messages, to combat reports, to Ship 0042 has completed construction).
GEEK CODE V.3.12: GCS/E d-- s: a-- C++ US+ P+ L++ E--- W+++ N+ !o? K- w-- !O M++ V? PS+ PE Y+ PGP t- 5++ X R !tv-- b+++ DI++ D+ G+ e+++ h !r*-- y?
SE4 CODE: A-- Se+++* GdY $?/++ Fr! C++* Css Sf Ai Au- M+ MpN S Ss- RV Pw- Fq-- Nd Rp+ G- Mm++ Bb@ Tcp- L+