•Assume A, B agree on all sentences in FOk
•Then, for every n ¸ 0, they agree on all sentences in Lk1,w of qr · n
–Why ? Consider Çi 2 I fi where 8 i. qr(fi) · n. Then this
is in FOk !
•Hence, for every n ¸ 0, A º1wk,nB
•Hence, A º1wk B
–Why ? Remember Koenig’s Lemma ?
•Hence A, B agree on all sentences in Lk1,w