id sid tid token lemma pos 9z902z12x9k 1 1 we we PRON 9z902z12x9k 1 2 examine examine VERB 9z902z12x9k 1 3 the the DET 9z902z12x9k 1 4 relation relation NOUN 9z902z12x9k 1 5 between between ADP 9z902z12x9k 1 6 the the DET 9z902z12x9k 1 7 uniformity uniformity NOUN 9z902z12x9k 1 8 of of ADP 9z902z12x9k 1 9 a a DET 9z902z12x9k 1 10 collection collection NOUN 9z902z12x9k 1 11 of of ADP 9z902z12x9k 1 12 operators operator NOUN 9z902z12x9k 1 13 witnessingturing witnessingture VERB 9z902z12x9k 1 14 computable computable ADJ 9z902z12x9k 1 15 embeddings embedding NOUN 9z902z12x9k 1 16 , , PUNCT 9z902z12x9k 1 17 and and CCONJ 9z902z12x9k 1 18 the the DET 9z902z12x9k 1 19 existence existence NOUN 9z902z12x9k 1 20 of of ADP 9z902z12x9k 1 21 an an DET 9z902z12x9k 1 22 operator operator NOUN 9z902z12x9k 1 23 witnessingthe witnessingthe NOUN 9z902z12x9k 1 24 universality universality NOUN 9z902z12x9k 1 25 of of ADP 9z902z12x9k 1 26 a a DET 9z902z12x9k 1 27 class class NOUN 9z902z12x9k 1 28 . . PUNCT 9z902z12x9k 2 1 the the DET 9z902z12x9k 2 2 primary primary ADJ 9z902z12x9k 2 3 equivalence equivalence NOUN 9z902z12x9k 2 4 relation relation NOUN 9z902z12x9k 2 5 studied study VERB 9z902z12x9k 2 6 here here ADV 9z902z12x9k 2 7 is be AUX 9z902z12x9k 2 8 computableinfinitary computableinfinitary ADJ 9z902z12x9k 2 9 σα σα PROPN 9z902z12x9k 2 10 equivalence equivalence NOUN 9z902z12x9k 2 11 . . PUNCT 9z902z12x9k 3 1 this this DET 9z902z12x9k 3 2 project project NOUN 9z902z12x9k 3 3 of of ADP 9z902z12x9k 3 4 exploiting exploit VERB 9z902z12x9k 3 5 uniformity uniformity NOUN 9z902z12x9k 3 6 of of ADP 9z902z12x9k 3 7 turingcomputable turingcomputable ADJ 9z902z12x9k 3 8 embeddings embedding NOUN 9z902z12x9k 3 9 to to PART 9z902z12x9k 3 10 construct construct VERB 9z902z12x9k 3 11 a a DET 9z902z12x9k 3 12 limit limit NOUN 9z902z12x9k 3 13 embedding embed VERB 9z902z12x9k 3 14 is be AUX 9z902z12x9k 3 15 carried carry VERB 9z902z12x9k 3 16 out out ADP 9z902z12x9k 3 17 entirely entirely ADV 9z902z12x9k 3 18 in in ADP 9z902z12x9k 3 19 thecontext thecontext NOUN 9z902z12x9k 3 20 of of ADP 9z902z12x9k 3 21 countable countable ADJ 9z902z12x9k 3 22 reduced reduce VERB 9z902z12x9k 3 23 abelian abelian ADJ 9z902z12x9k 3 24 p p NOUN 9z902z12x9k 3 25 - - PUNCT 9z902z12x9k 3 26 groups group NOUN 9z902z12x9k 3 27 . . PUNCT 9z902z12x9k 4 1 one one PRON 9z902z12x9k 4 2 may may AUX 9z902z12x9k 4 3 look look VERB 9z902z12x9k 4 4 at at ADP 9z902z12x9k 4 5 this this DET 9z902z12x9k 4 6 program program NOUN 9z902z12x9k 4 7 as as ADP 9z902z12x9k 4 8 eithera eithera PROPN 9z902z12x9k 4 9 project project NOUN 9z902z12x9k 4 10 in in ADP 9z902z12x9k 4 11 the the DET 9z902z12x9k 4 12 computable computable ADJ 9z902z12x9k 4 13 structure structure NOUN 9z902z12x9k 4 14 theory theory NOUN 9z902z12x9k 4 15 of of ADP 9z902z12x9k 4 16 abelian abelian ADJ 9z902z12x9k 4 17 p p NOUN 9z902z12x9k 4 18 - - PUNCT 9z902z12x9k 4 19 groups group NOUN 9z902z12x9k 4 20 , , PUNCT 9z902z12x9k 4 21 or or CCONJ 9z902z12x9k 4 22 as as ADP 9z902z12x9k 4 23 a a DET 9z902z12x9k 4 24 projectin projectin NOUN 9z902z12x9k 4 25 the the DET 9z902z12x9k 4 26 construction construction NOUN 9z902z12x9k 4 27 of of ADP 9z902z12x9k 4 28 limits limit NOUN 9z902z12x9k 4 29 of of ADP 9z902z12x9k 4 30 sequences sequence NOUN 9z902z12x9k 4 31 of of ADP 9z902z12x9k 4 32 uniform uniform NOUN 9z902z12x9k 4 33 turing ture VERB 9z902z12x9k 4 34 computable computable ADJ 9z902z12x9k 4 35 operators operator NOUN 9z902z12x9k 4 36 . . PUNCT 9z902z12x9k 5 1 in in ADP 9z902z12x9k 5 2 an an DET 9z902z12x9k 5 3 attempt attempt NOUN 9z902z12x9k 5 4 to to PART 9z902z12x9k 5 5 explore explore VERB 9z902z12x9k 5 6 the the DET 9z902z12x9k 5 7 boundary boundary NOUN 9z902z12x9k 5 8 between between ADP 9z902z12x9k 5 9 computable computable PROPN 9z902z12x9k 5 10 infinitary infinitary ADJ 9z902z12x9k 5 11 σα σα PROPN 9z902z12x9k 5 12 equivalenceand equivalenceand PROPN 9z902z12x9k 5 13 isomorphism isomorphism NOUN 9z902z12x9k 5 14 , , PUNCT 9z902z12x9k 5 15 we we PRON 9z902z12x9k 5 16 show show VERB 9z902z12x9k 5 17 that that SCONJ 9z902z12x9k 5 18 for for ADP 9z902z12x9k 5 19 any any DET 9z902z12x9k 5 20 computable computable NOUN 9z902z12x9k 5 21 , , PUNCT 9z902z12x9k 5 22 certain certain ADJ 9z902z12x9k 5 23 classes class NOUN 9z902z12x9k 5 24 of of ADP 9z902z12x9k 5 25 countablereduced countablereduced ADJ 9z902z12x9k 5 26 abelian abelian ADJ 9z902z12x9k 5 27 p p NOUN 9z902z12x9k 5 28 - - PUNCT 9z902z12x9k 5 29 groups group NOUN 9z902z12x9k 5 30 are be AUX 9z902z12x9k 5 31 universal universal ADJ 9z902z12x9k 5 32 for for ADP 9z902z12x9k 5 33 ∼cα ∼cα NOUN 9z902z12x9k 5 34 under under ADP 9z902z12x9k 5 35 turing ture VERB 9z902z12x9k 5 36 computable computable ADJ 9z902z12x9k 5 37 embedding.further embedding.further NOUN 9z902z12x9k 5 38 , , PUNCT 9z902z12x9k 5 39 the the DET 9z902z12x9k 5 40 operators operator NOUN 9z902z12x9k 5 41 witnessing witness VERB 9z902z12x9k 5 42 these these DET 9z902z12x9k 5 43 embeddings embedding NOUN 9z902z12x9k 5 44 are be AUX 9z902z12x9k 5 45 extremely extremely ADV 9z902z12x9k 5 46 uniform uniform ADJ 9z902z12x9k 5 47 . . PUNCT 9z902z12x9k 6 1 exploiting exploit VERB 9z902z12x9k 6 2 the the DET 9z902z12x9k 6 3 uniformity uniformity NOUN 9z902z12x9k 6 4 of of ADP 9z902z12x9k 6 5 the the DET 9z902z12x9k 6 6 embeddings embedding NOUN 9z902z12x9k 6 7 , , PUNCT 9z902z12x9k 6 8 we we PRON 9z902z12x9k 6 9 produce produce VERB 9z902z12x9k 6 10 operators operator NOUN 9z902z12x9k 6 11 which which PRON 9z902z12x9k 6 12 are be AUX 9z902z12x9k 6 13 , , PUNCT 9z902z12x9k 6 14 in in ADP 9z902z12x9k 6 15 some some DET 9z902z12x9k 6 16 sense sense NOUN 9z902z12x9k 6 17 , , PUNCT 9z902z12x9k 6 18 limits limit NOUN 9z902z12x9k 6 19 of of ADP 9z902z12x9k 6 20 the the DET 9z902z12x9k 6 21 embeddings embedding NOUN 9z902z12x9k 6 22 witnessing witness VERB 9z902z12x9k 6 23 the the DET 9z902z12x9k 6 24 universality universality NOUN 9z902z12x9k 6 25 of of ADP 9z902z12x9k 6 26 the the DET 9z902z12x9k 6 27 classesof classesof VERB 9z902z12x9k 6 28 countable countable ADJ 9z902z12x9k 6 29 reduced reduce VERB 9z902z12x9k 6 30 abelian abelian ADJ 9z902z12x9k 6 31 p p NOUN 9z902z12x9k 6 32 - - PUNCT 9z902z12x9k 6 33 groups group NOUN 9z902z12x9k 6 34 . . PUNCT 9z902z12x9k 7 1 this this PRON 9z902z12x9k 7 2 is be AUX 9z902z12x9k 7 3 approached approach VERB 9z902z12x9k 7 4 in in ADP 9z902z12x9k 7 5 three three NUM 9z902z12x9k 7 6 dierent dierent ADJ 9z902z12x9k 7 7 ways way NOUN 9z902z12x9k 7 8 : : PUNCT 9z902z12x9k 7 9 transnite transnite ADJ 9z902z12x9k 7 10 recursion recursion NOUN 9z902z12x9k 7 11 on on ADP 9z902z12x9k 7 12 ordinal ordinal ADJ 9z902z12x9k 7 13 notation notation NOUN 9z902z12x9k 7 14 , , PUNCT 9z902z12x9k 7 15 barwise barwise PROPN 9z902z12x9k 7 16 - - PUNCT 9z902z12x9k 7 17 kreisel kreisel PROPN 9z902z12x9k 7 18 compactness compactness NOUN 9z902z12x9k 7 19 , , PUNCT 9z902z12x9k 7 20 and and CCONJ 9z902z12x9k 7 21 hyperarithemeticalsaturation hyperarithemeticalsaturation NOUN 9z902z12x9k 7 22 . . PUNCT 9z902z12x9k 8 1 finally finally ADV 9z902z12x9k 8 2 , , PUNCT 9z902z12x9k 8 3 we we PRON 9z902z12x9k 8 4 work work VERB 9z902z12x9k 8 5 in in ADP 9z902z12x9k 8 6 admissible admissible ADJ 9z902z12x9k 8 7 set set NOUN 9z902z12x9k 8 8 theory theory NOUN 9z902z12x9k 8 9 , , PUNCT 9z902z12x9k 8 10 and and CCONJ 9z902z12x9k 8 11 use use VERB 9z902z12x9k 8 12 barwisecompactness barwisecompactness NOUN 9z902z12x9k 8 13 and and CCONJ 9z902z12x9k 8 14 σa σa NOUN 9z902z12x9k 8 15 - - NOUN 9z902z12x9k 8 16 saturation saturation NOUN 9z902z12x9k 8 17 to to PART 9z902z12x9k 8 18 generalize generalize VERB 9z902z12x9k 8 19 selected select VERB 9z902z12x9k 8 20 results result NOUN 9z902z12x9k 8 21 . . PUNCT