id sid tid token lemma pos q237hq4084w 1 1 recently recently ADV q237hq4084w 1 2 , , PUNCT q237hq4084w 1 3 researchers researcher NOUN q237hq4084w 1 4 in in ADP q237hq4084w 1 5 the the DET q237hq4084w 1 6 foundations foundation NOUN q237hq4084w 1 7 of of ADP q237hq4084w 1 8 mathematics mathematic NOUN q237hq4084w 1 9 have have AUX q237hq4084w 1 10 become become VERB q237hq4084w 1 11 interested interested ADJ q237hq4084w 1 12 in in ADP q237hq4084w 1 13 the the DET q237hq4084w 1 14 distributive distributive ADJ q237hq4084w 1 15 lattices lattice NOUN q237hq4084w 1 16 pw pw PROPN q237hq4084w 1 17 and and CCONJ q237hq4084w 1 18 ps ps PROPN q237hq4084w 1 19 , , PUNCT q237hq4084w 1 20 the the DET q237hq4084w 1 21 study study NOUN q237hq4084w 1 22 of of ADP q237hq4084w 1 23 which which PRON q237hq4084w 1 24 is be AUX q237hq4084w 1 25 a a DET q237hq4084w 1 26 major major ADJ q237hq4084w 1 27 part part NOUN q237hq4084w 1 28 of of ADP q237hq4084w 1 29 the the DET q237hq4084w 1 30 field field NOUN q237hq4084w 1 31 of of ADP q237hq4084w 1 32 & & CCONJ q237hq4084w 1 33 quot;mass quot;mass PROPN q237hq4084w 1 34 problems." problems." PROPN q237hq4084w 1 35 ; ; PUNCT q237hq4084w 1 36 in in ADP q237hq4084w 1 37 general general ADJ q237hq4084w 1 38 , , PUNCT q237hq4084w 1 39 a a DET q237hq4084w 1 40 mass mass NOUN q237hq4084w 1 41 problem problem NOUN q237hq4084w 1 42 u u PROPN q237hq4084w 1 43 is be AUX q237hq4084w 1 44 a a DET q237hq4084w 1 45 subset subset NOUN q237hq4084w 1 46 of of ADP q237hq4084w 1 47 & & CCONJ q237hq4084w 1 48 omega;&omega omega;&omega PROPN q237hq4084w 1 49 ; ; PUNCT q237hq4084w 1 50 ( ( PUNCT q237hq4084w 1 51 baire baire NOUN q237hq4084w 1 52 space space NOUN q237hq4084w 1 53 ) ) PUNCT q237hq4084w 1 54 . . PUNCT q237hq4084w 2 1 we we PRON q237hq4084w 2 2 define define VERB q237hq4084w 2 3 u u PROPN q237hq4084w 2 4 & & CCONJ q237hq4084w 2 5 le;s le;s PROPN q237hq4084w 2 6 v v NOUN q237hq4084w 2 7 if if SCONJ q237hq4084w 2 8 there there PRON q237hq4084w 2 9 is be VERB q237hq4084w 2 10 an an DET q237hq4084w 2 11 index index NOUN q237hq4084w 2 12 e e NOUN q237hq4084w 2 13 for for ADP q237hq4084w 2 14 a a DET q237hq4084w 2 15 computable computable ADJ q237hq4084w 2 16 functional functional NOUN q237hq4084w 2 17 so so SCONJ q237hq4084w 2 18 that that SCONJ q237hq4084w 2 19 for for ADP q237hq4084w 2 20 all all DET q237hq4084w 2 21 f f PROPN q237hq4084w 2 22 & & CCONJ q237hq4084w 2 23 isin isin PROPN q237hq4084w 2 24 ; ; PUNCT q237hq4084w 2 25 v v PROPN q237hq4084w 2 26 , , PUNCT q237hq4084w 2 27 & & CCONJ q237hq4084w 2 28 phi;ef phi;ef PROPN q237hq4084w 2 29 & & CCONJ q237hq4084w 2 30 isin isin PROPN q237hq4084w 2 31 ; ; PUNCT q237hq4084w 2 32 u. u. PROPN q237hq4084w 2 33 if if SCONJ q237hq4084w 2 34 we we PRON q237hq4084w 2 35 do do AUX q237hq4084w 2 36 not not PART q237hq4084w 2 37 require require VERB q237hq4084w 2 38 the the DET q237hq4084w 2 39 same same ADJ q237hq4084w 2 40 e e NOUN q237hq4084w 2 41 for for ADP q237hq4084w 2 42 every every DET q237hq4084w 2 43 f f PROPN q237hq4084w 2 44 , , PUNCT q237hq4084w 2 45 we we PRON q237hq4084w 2 46 get get VERB q237hq4084w 2 47 a a PRON q237hq4084w 2 48 & & CCONJ q237hq4084w 2 49 quot;weak quot;weak NOUN q237hq4084w 2 50 version" version" SPACE q237hq4084w 2 51 ; ; PUNCT q237hq4084w 2 52 : : PUNCT q237hq4084w 2 53 u u PROPN q237hq4084w 2 54 & & CCONJ q237hq4084w 2 55 lew lew PROPN q237hq4084w 2 56 v v PROPN q237hq4084w 2 57 if if SCONJ q237hq4084w 2 58 for for ADP q237hq4084w 2 59 all all DET q237hq4084w 2 60 f f PROPN q237hq4084w 2 61 & & CCONJ q237hq4084w 2 62 isin isin PROPN q237hq4084w 2 63 ; ; PUNCT q237hq4084w 2 64 v v PROPN q237hq4084w 2 65 , , PUNCT q237hq4084w 2 66 there there PRON q237hq4084w 2 67 is be VERB q237hq4084w 2 68 an an DET q237hq4084w 2 69 e e NOUN q237hq4084w 2 70 so so SCONJ q237hq4084w 2 71 that that PRON q237hq4084w 2 72 & & CCONJ q237hq4084w 2 73 phi;ef phi;ef PROPN q237hq4084w 2 74 & & CCONJ q237hq4084w 2 75 isin isin PROPN q237hq4084w 2 76 ; ; PUNCT q237hq4084w 2 77 u. u. PROPN q237hq4084w 2 78 the the DET q237hq4084w 2 79 relations relation NOUN q237hq4084w 2 80 & & CCONJ q237hq4084w 2 81 le;s le;s NOUN q237hq4084w 2 82 and and CCONJ q237hq4084w 2 83 & & CCONJ q237hq4084w 2 84 le;w le;w NOUN q237hq4084w 2 85 naturally naturally ADV q237hq4084w 2 86 induce induce VERB q237hq4084w 2 87 equivalence equivalence NOUN q237hq4084w 2 88 relations relation NOUN q237hq4084w 2 89 & & CCONJ q237hq4084w 2 90 equiv;s equiv;s PROPN q237hq4084w 2 91 and and CCONJ q237hq4084w 2 92 & & CCONJ q237hq4084w 2 93 equiv;w equiv;w PROPN q237hq4084w 2 94 . . PUNCT q237hq4084w 3 1 we we PRON q237hq4084w 3 2 define define VERB q237hq4084w 3 3 ps ps PRON q237hq4084w 3 4 to to PART q237hq4084w 3 5 be be AUX q237hq4084w 3 6 the the DET q237hq4084w 3 7 collection collection NOUN q237hq4084w 3 8 of of ADP q237hq4084w 3 9 & & CCONJ q237hq4084w 3 10 equiv;s equiv;s PROPN q237hq4084w 3 11 degrees degree NOUN q237hq4084w 3 12 of of ADP q237hq4084w 3 13 nonempty nonempty ADJ q237hq4084w 3 14 & & CCONJ q237hq4084w 3 15 pi;01 pi;01 NOUN q237hq4084w 3 16 subsets subset NOUN q237hq4084w 3 17 of of ADP q237hq4084w 3 18 2&omega 2&omega NUM q237hq4084w 3 19 ; ; PUNCT q237hq4084w 3 20 ( ( PUNCT q237hq4084w 3 21 cantor cantor PROPN q237hq4084w 3 22 space space NOUN q237hq4084w 3 23 ) ) PUNCT q237hq4084w 3 24 ; ; PUNCT q237hq4084w 3 25 similarly similarly ADV q237hq4084w 3 26 , , PUNCT q237hq4084w 3 27 we we PRON q237hq4084w 3 28 define define VERB q237hq4084w 3 29 pw pw NOUN q237hq4084w 3 30 to to PART q237hq4084w 3 31 be be AUX q237hq4084w 3 32 the the DET q237hq4084w 3 33 collection collection NOUN q237hq4084w 3 34 of of ADP q237hq4084w 3 35 & & CCONJ q237hq4084w 3 36 equiv;w equiv;w PROPN q237hq4084w 3 37 degrees degree NOUN q237hq4084w 3 38 of of ADP q237hq4084w 3 39 nonempty nonempty ADJ q237hq4084w 3 40 & & CCONJ q237hq4084w 3 41 pi;01 pi;01 NOUN q237hq4084w 3 42 subsets subset NOUN q237hq4084w 3 43 of of ADP q237hq4084w 3 44 2&omega 2&omega NUM q237hq4084w 3 45 ; ; PUNCT q237hq4084w 3 46 . . PUNCT q237hq4084w 4 1 an an DET q237hq4084w 4 2 important important ADJ q237hq4084w 4 3 open open ADJ q237hq4084w 4 4 question question NOUN q237hq4084w 4 5 is be AUX q237hq4084w 4 6 whether whether SCONJ q237hq4084w 4 7 pw pw X q237hq4084w 4 8 is be AUX q237hq4084w 4 9 dense dense ADJ q237hq4084w 4 10 . . PUNCT q237hq4084w 5 1 the the DET q237hq4084w 5 2 result result NOUN q237hq4084w 5 3 of of ADP q237hq4084w 5 4 chapter chapter NOUN q237hq4084w 5 5 2 2 NUM q237hq4084w 5 6 is be AUX q237hq4084w 5 7 that that SCONJ q237hq4084w 5 8 the the DET q237hq4084w 5 9 embedding embedding NOUN q237hq4084w 5 10 of of ADP q237hq4084w 5 11 the the DET q237hq4084w 5 12 free free ADJ q237hq4084w 5 13 distributive distributive ADJ q237hq4084w 5 14 lattice lattice NOUN q237hq4084w 5 15 on on ADP q237hq4084w 5 16 countably countably ADV q237hq4084w 5 17 many many ADJ q237hq4084w 5 18 generators generator NOUN q237hq4084w 5 19 into into ADP q237hq4084w 5 20 ps ps PROPN q237hq4084w 5 21 can can AUX q237hq4084w 5 22 be be AUX q237hq4084w 5 23 done do VERB q237hq4084w 5 24 densely densely ADV q237hq4084w 5 25 . . PUNCT q237hq4084w 6 1 the the DET q237hq4084w 6 2 way way NOUN q237hq4084w 6 3 it it PRON q237hq4084w 6 4 is be AUX q237hq4084w 6 5 done do VERB q237hq4084w 6 6 gives give VERB q237hq4084w 6 7 indirect indirect ADJ q237hq4084w 6 8 evidence evidence NOUN q237hq4084w 6 9 that that SCONJ q237hq4084w 6 10 the the DET q237hq4084w 6 11 kinds kind NOUN q237hq4084w 6 12 of of ADP q237hq4084w 6 13 priority priority NOUN q237hq4084w 6 14 arguments argument NOUN q237hq4084w 6 15 that that PRON q237hq4084w 6 16 show show VERB q237hq4084w 6 17 the the DET q237hq4084w 6 18 density density NOUN q237hq4084w 6 19 of of ADP q237hq4084w 6 20 ps ps PRON q237hq4084w 6 21 are be AUX q237hq4084w 6 22 probably probably ADV q237hq4084w 6 23 not not PART q237hq4084w 6 24 strong strong ADJ q237hq4084w 6 25 enough enough ADV q237hq4084w 6 26 to to PART q237hq4084w 6 27 show show VERB q237hq4084w 6 28 the the DET q237hq4084w 6 29 density density NOUN q237hq4084w 6 30 of of ADP q237hq4084w 6 31 pw pw PROPN q237hq4084w 6 32 . . PUNCT q237hq4084w 7 1 the the DET q237hq4084w 7 2 result result NOUN q237hq4084w 7 3 of of ADP q237hq4084w 7 4 chapter chapter NOUN q237hq4084w 7 5 3 3 NUM q237hq4084w 7 6 applies apply VERB q237hq4084w 7 7 these these DET q237hq4084w 7 8 priority priority NOUN q237hq4084w 7 9 arguments argument NOUN q237hq4084w 7 10 to to PART q237hq4084w 7 11 show show VERB q237hq4084w 7 12 the the DET q237hq4084w 7 13 decidability decidability NOUN q237hq4084w 7 14 of of ADP q237hq4084w 7 15 the the DET q237hq4084w 7 16 elementary elementary PROPN q237hq4084w 7 17 & & CCONJ q237hq4084w 7 18 forall;∃-theory forall;∃-theory PROPN q237hq4084w 7 19 of of ADP q237hq4084w 7 20 ps ps PROPN q237hq4084w 7 21 as as ADP q237hq4084w 7 22 a a DET q237hq4084w 7 23 partial partial ADJ q237hq4084w 7 24 order order NOUN q237hq4084w 7 25 . . PUNCT q237hq4084w 8 1 the the DET q237hq4084w 8 2 result result NOUN q237hq4084w 8 3 of of ADP q237hq4084w 8 4 chapter chapter NOUN q237hq4084w 8 5 5 5 NUM q237hq4084w 8 6 is be AUX q237hq4084w 8 7 that that SCONJ q237hq4084w 8 8 certain certain ADJ q237hq4084w 8 9 index index NOUN q237hq4084w 8 10 sets set NOUN q237hq4084w 8 11 related relate VERB q237hq4084w 8 12 to to ADP q237hq4084w 8 13 pw pw X q237hq4084w 8 14 are be AUX q237hq4084w 8 15 & & CCONJ q237hq4084w 8 16 pi;11 pi;11 SPACE q237hq4084w 8 17 - - PUNCT q237hq4084w 8 18 complete complete ADJ q237hq4084w 8 19 . . PUNCT q237hq4084w 9 1 this this PRON q237hq4084w 9 2 leads lead VERB q237hq4084w 9 3 to to ADP q237hq4084w 9 4 a a DET q237hq4084w 9 5 conjecture conjecture NOUN q237hq4084w 9 6 that that SCONJ q237hq4084w 9 7 the the DET q237hq4084w 9 8 turing turing NOUN q237hq4084w 9 9 degree degree NOUN q237hq4084w 9 10 of of ADP q237hq4084w 9 11 its its PRON q237hq4084w 9 12 elementary elementary ADJ q237hq4084w 9 13 theory theory NOUN q237hq4084w 9 14 is be AUX q237hq4084w 9 15 as as ADV q237hq4084w 9 16 high high ADJ q237hq4084w 9 17 as as ADP q237hq4084w 9 18 possible possible ADJ q237hq4084w 9 19 . . PUNCT