The Borde-Goothed-Filenkin Theorem in Extended Decider Spaces

The Borde-Goothed-Filenkin theorem states that the universe's geodesically complete IE had to have a beginning. Oleg Kuznetsov: I wonder whether there's a contradiction here between these models or are they compatible? He says it does get rid of infinity in the sense of an infinite number of states but the universe still lasts eternally, even if time steps are discrete according to the evolution. But what do we learn from saying that? Can we say that the universe therefore had a beginning? he asks.