<ClemA>Do you want me to guess how your often illogically thinking brain got it wrong again?
Congrats on your - blind - faith in a guy named Danker. Others prefer to put their - both eyes closed - faith in one of the Pontiffs or Old Slewfoot.
I've already posted many remarks in opposition to many of the BDAG cites conclusions. I have done this with facts, info from scholars, ECF, logic & Scripture, etc. I have also quoted scholars who remark upon the weaknesses, errors & inadequacies of lexicons in general, including BDAG.
Why doesn't BDAG list the following dozens of "ancient sources cited under aionios"? Did the author purposely omit them to weigh the evidence according to his biases? To sell books?
Ask yourself the same regarding the following you posted from BDAG.
You & Danker have provided - no evidence - that any of those references should be interpreted to mean "pert. to a period of unending duration, without end". Anyone can post a bunch of references & make all kinds of claims about what they mean. Proving it from context is something else completely. And, BTW, lexicons & scholars are often in disagreement with each other re aionios. Even those that are biased to endless hell are in much disharmony amongst themselves on various points re aionios.
Furthermore, the dishonesty of Danker can be seen in his only cite of Origen above under aionios saying "in the Reign of God: ζωὴ αἰ. (Orig., C. Cels. 2, 77, 3)", while ignoring all Origen's references to aionios that are finite, as i've documented here:
BDAG's entry above re aionios has many cites from Diodorus Siculus, Philo & Josephus. There again Danker omits examples where such authors use aionios of finite duration. For example, see the reference to Philo at the above url.
Moreover you have your rare theory that aion & aionios always mean eternal unless used in hyperbole. Generally scholars, including BDAG, oppose your opinion.<end>
This discussion is over. You, with zero formal education or expertise in Koine Greek, who probably could not parse a Greek verb if your life depended on it, have set yourself up as an expert,