id sid tid token lemma pos c821gh95k40 1 1 mathematicians mathematician NOUN c821gh95k40 1 2 of of ADP c821gh95k40 1 3 all all DET c821gh95k40 1 4 sorts sort NOUN c821gh95k40 1 5 participate participate VERB c821gh95k40 1 6 in in ADP c821gh95k40 1 7 the the DET c821gh95k40 1 8 search search NOUN c821gh95k40 1 9 to to PART c821gh95k40 1 10 classify classify VERB c821gh95k40 1 11 structures structure NOUN c821gh95k40 1 12 and and CCONJ c821gh95k40 1 13 characterize characterize VERB c821gh95k40 1 14 the the DET c821gh95k40 1 15 structures structure NOUN c821gh95k40 1 16 which which PRON c821gh95k40 1 17 belong belong VERB c821gh95k40 1 18 to to ADP c821gh95k40 1 19 a a DET c821gh95k40 1 20 class class NOUN c821gh95k40 1 21 . . PUNCT c821gh95k40 2 1 logicians logician NOUN c821gh95k40 2 2 have have AUX c821gh95k40 2 3 worked work VERB c821gh95k40 2 4 on on ADP c821gh95k40 2 5 finding find VERB c821gh95k40 2 6 the the DET c821gh95k40 2 7 complexity complexity NOUN c821gh95k40 2 8 of of ADP c821gh95k40 2 9 the the DET c821gh95k40 2 10 isomorphism isomorphism NOUN c821gh95k40 2 11 relation relation NOUN c821gh95k40 2 12 on on ADP c821gh95k40 2 13 a a DET c821gh95k40 2 14 class class NOUN c821gh95k40 2 15 of of ADP c821gh95k40 2 16 structures structure NOUN c821gh95k40 2 17 , , PUNCT c821gh95k40 2 18 the the DET c821gh95k40 2 19 " " PUNCT c821gh95k40 2 20 classification classification NOUN c821gh95k40 2 21 problem problem NOUN c821gh95k40 2 22 , , PUNCT c821gh95k40 2 23 " " PUNCT c821gh95k40 2 24 and and CCONJ c821gh95k40 2 25 categorizing categorize VERB c821gh95k40 2 26 the the DET c821gh95k40 2 27 relative relative ADJ c821gh95k40 2 28 complexity complexity NOUN c821gh95k40 2 29 of of ADP c821gh95k40 2 30 the the DET c821gh95k40 2 31 isomorphism isomorphism NOUN c821gh95k40 2 32 relation relation NOUN c821gh95k40 2 33 on on ADP c821gh95k40 2 34 different different ADJ c821gh95k40 2 35 classes class NOUN c821gh95k40 2 36 of of ADP c821gh95k40 2 37 structures structure NOUN c821gh95k40 2 38 . . PUNCT c821gh95k40 3 1 one one NUM c821gh95k40 3 2 way way NOUN c821gh95k40 3 3 of of ADP c821gh95k40 3 4 comparing compare VERB c821gh95k40 3 5 the the DET c821gh95k40 3 6 complexity complexity NOUN c821gh95k40 3 7 of of ADP c821gh95k40 3 8 the the DET c821gh95k40 3 9 classification classification NOUN c821gh95k40 3 10 problem problem NOUN c821gh95k40 3 11 for for ADP c821gh95k40 3 12 different different ADJ c821gh95k40 3 13 classes class NOUN c821gh95k40 3 14 of of ADP c821gh95k40 3 15 structures structure NOUN c821gh95k40 3 16 uses use VERB c821gh95k40 3 17 the the DET c821gh95k40 3 18 notion notion NOUN c821gh95k40 3 19 of of ADP c821gh95k40 3 20 a a DET c821gh95k40 3 21 turing ture VERB c821gh95k40 3 22 computable computable NOUN c821gh95k40 3 23 embedding.this embedding.this NOUN c821gh95k40 3 24 notion notion NOUN c821gh95k40 3 25 allows allow VERB c821gh95k40 3 26 us we PRON c821gh95k40 3 27 to to PART c821gh95k40 3 28 compare compare VERB c821gh95k40 3 29 the the DET c821gh95k40 3 30 complexity complexity NOUN c821gh95k40 3 31 of of ADP c821gh95k40 3 32 the the DET c821gh95k40 3 33 classification classification NOUN c821gh95k40 3 34 problem problem NOUN c821gh95k40 3 35 for for ADP c821gh95k40 3 36 certain certain ADJ c821gh95k40 3 37 classes class NOUN c821gh95k40 3 38 of of ADP c821gh95k40 3 39 structures structure NOUN c821gh95k40 3 40 , , PUNCT c821gh95k40 3 41 and and CCONJ c821gh95k40 3 42 make make VERB c821gh95k40 3 43 some some DET c821gh95k40 3 44 distinctions distinction NOUN c821gh95k40 3 45 that that PRON c821gh95k40 3 46 can can AUX c821gh95k40 3 47 not not PART c821gh95k40 3 48 be be AUX c821gh95k40 3 49 made make VERB c821gh95k40 3 50 under under ADP c821gh95k40 3 51 the the DET c821gh95k40 3 52 notion notion NOUN c821gh95k40 3 53 of of ADP c821gh95k40 3 54 borel borel PROPN c821gh95k40 3 55 embedding embedding PROPN c821gh95k40 3 56 . . PUNCT c821gh95k40 4 1 the the DET c821gh95k40 4 2 main main ADJ c821gh95k40 4 3 tool tool NOUN c821gh95k40 4 4 in in ADP c821gh95k40 4 5 making make VERB c821gh95k40 4 6 those those DET c821gh95k40 4 7 distinctions distinction NOUN c821gh95k40 4 8 , , PUNCT c821gh95k40 4 9 i.e. i.e. X c821gh95k40 4 10 in in ADP c821gh95k40 4 11 showing show VERB c821gh95k40 4 12 non non ADJ c821gh95k40 4 13 - - NOUN c821gh95k40 4 14 embeddability embeddability NOUN c821gh95k40 4 15 between between ADP c821gh95k40 4 16 one one NUM c821gh95k40 4 17 class class NOUN c821gh95k40 4 18 of of ADP c821gh95k40 4 19 structures structure NOUN c821gh95k40 4 20 and and CCONJ c821gh95k40 4 21 another another PRON c821gh95k40 4 22 , , PUNCT c821gh95k40 4 23 is be AUX c821gh95k40 4 24 the the DET c821gh95k40 4 25 pull pull VERB c821gh95k40 4 26 - - PUNCT c821gh95k40 4 27 back back NOUN c821gh95k40 4 28 theorem theorem NOUN c821gh95k40 4 29 . . PUNCT c821gh95k40 5 1 the the DET c821gh95k40 5 2 pull pull VERB c821gh95k40 5 3 - - PUNCT c821gh95k40 5 4 back back NOUN c821gh95k40 5 5 theorem theorem NOUN c821gh95k40 5 6 for for ADP c821gh95k40 5 7 turing ture VERB c821gh95k40 5 8 computable computable ADJ c821gh95k40 5 9 embeddings embedding NOUN c821gh95k40 5 10 says say VERB c821gh95k40 5 11 that that SCONJ c821gh95k40 5 12 if if SCONJ c821gh95k40 5 13 there there PRON c821gh95k40 5 14 is be VERB c821gh95k40 5 15 a a DET c821gh95k40 5 16 turing ture VERB c821gh95k40 5 17 computable computable NOUN c821gh95k40 5 18 embedding embedding NOUN c821gh95k40 5 19 between between ADP c821gh95k40 5 20 k k PROPN c821gh95k40 5 21 and and CCONJ c821gh95k40 5 22 k k PROPN c821gh95k40 5 23 ' ' PUNCT c821gh95k40 5 24 , , PUNCT c821gh95k40 5 25 then then ADV c821gh95k40 5 26 anything anything PRON c821gh95k40 5 27 you you PRON c821gh95k40 5 28 can can AUX c821gh95k40 5 29 say say VERB c821gh95k40 5 30 in in ADP c821gh95k40 5 31 the the DET c821gh95k40 5 32 language language NOUN c821gh95k40 5 33 of of ADP c821gh95k40 5 34 k k PROPN c821gh95k40 5 35 ' ' PUNCT c821gh95k40 5 36 you you PRON c821gh95k40 5 37 can can AUX c821gh95k40 5 38 " " PUNCT c821gh95k40 5 39 pull pull VERB c821gh95k40 5 40 back back ADV c821gh95k40 5 41 " " PUNCT c821gh95k40 5 42 and and CCONJ c821gh95k40 5 43 say say VERB c821gh95k40 5 44 in in ADP c821gh95k40 5 45 the the DET c821gh95k40 5 46 language language NOUN c821gh95k40 5 47 of of ADP c821gh95k40 5 48 k k PROPN c821gh95k40 5 49 , , PUNCT c821gh95k40 5 50 with with ADP c821gh95k40 5 51 the the DET c821gh95k40 5 52 same same ADJ c821gh95k40 5 53 complexity complexity NOUN c821gh95k40 5 54 . . PUNCT c821gh95k40 6 1 in in ADP c821gh95k40 6 2 this this DET c821gh95k40 6 3 work work NOUN c821gh95k40 6 4 , , PUNCT c821gh95k40 6 5 i i PRON c821gh95k40 6 6 consider consider VERB c821gh95k40 6 7 classes class NOUN c821gh95k40 6 8 of of ADP c821gh95k40 6 9 structures structure NOUN c821gh95k40 6 10 with with ADP c821gh95k40 6 11 countable countable ADJ c821gh95k40 6 12 universe universe NOUN c821gh95k40 6 13 , , PUNCT c821gh95k40 6 14 develop develop VERB c821gh95k40 6 15 more more ADJ c821gh95k40 6 16 general general ADJ c821gh95k40 6 17 notions notion NOUN c821gh95k40 6 18 of of ADP c821gh95k40 6 19 embeddings embedding NOUN c821gh95k40 6 20 between between ADP c821gh95k40 6 21 these these DET c821gh95k40 6 22 classes class NOUN c821gh95k40 6 23 , , PUNCT c821gh95k40 6 24 and and CCONJ c821gh95k40 6 25 prove prove VERB c821gh95k40 6 26 corresponding correspond VERB c821gh95k40 6 27 pull pull NOUN c821gh95k40 6 28 - - PUNCT c821gh95k40 6 29 back back NOUN c821gh95k40 6 30 theorems.i theorems.i NOUN c821gh95k40 6 31 also also ADV c821gh95k40 6 32 present present VERB c821gh95k40 6 33 a a DET c821gh95k40 6 34 result result NOUN c821gh95k40 6 35 on on ADP c821gh95k40 6 36 the the DET c821gh95k40 6 37 complexity complexity NOUN c821gh95k40 6 38 of of ADP c821gh95k40 6 39 computable computable ADJ c821gh95k40 6 40 isomorphism isomorphism NOUN c821gh95k40 6 41 on on ADP c821gh95k40 6 42 the the DET c821gh95k40 6 43 class class NOUN c821gh95k40 6 44 of of ADP c821gh95k40 6 45 boolean boolean ADJ c821gh95k40 6 46 algebras algebra NOUN c821gh95k40 6 47 , , PUNCT c821gh95k40 6 48 and and CCONJ c821gh95k40 6 49 joint joint ADJ c821gh95k40 6 50 work work NOUN c821gh95k40 6 51 on on ADP c821gh95k40 6 52 the the DET c821gh95k40 6 53 computable computable ADJ c821gh95k40 6 54 embedding embedding NOUN c821gh95k40 6 55 problem problem NOUN c821gh95k40 6 56 , , PUNCT c821gh95k40 6 57 considering consider VERB c821gh95k40 6 58 how how SCONJ c821gh95k40 6 59 hard hard ADJ c821gh95k40 6 60 it it PRON c821gh95k40 6 61 is be AUX c821gh95k40 6 62 to to PART c821gh95k40 6 63 tell tell VERB c821gh95k40 6 64 if if SCONJ c821gh95k40 6 65 one one NUM c821gh95k40 6 66 structure structure NOUN c821gh95k40 6 67 in in ADP c821gh95k40 6 68 a a DET c821gh95k40 6 69 class class NOUN c821gh95k40 6 70 is be AUX c821gh95k40 6 71 isomorphic isomorphic ADJ c821gh95k40 6 72 to to ADP c821gh95k40 6 73 a a DET c821gh95k40 6 74 substructure substructure NOUN c821gh95k40 6 75 of of ADP c821gh95k40 6 76 another another DET c821gh95k40 6 77 structure structure NOUN c821gh95k40 6 78 in in ADP c821gh95k40 6 79 the the DET c821gh95k40 6 80 class class NOUN c821gh95k40 6 81 . . PUNCT