id sid tid token lemma pos 4j03cz32m37 1 1 in in ADP 4j03cz32m37 1 2 the the DET 4j03cz32m37 1 3 philosophical philosophical ADJ 4j03cz32m37 1 4 portion portion NOUN 4j03cz32m37 1 5 of of ADP 4j03cz32m37 1 6 this this DET 4j03cz32m37 1 7 dissertation dissertation NOUN 4j03cz32m37 1 8 , , PUNCT 4j03cz32m37 1 9 i i PRON 4j03cz32m37 1 10 develop develop VERB 4j03cz32m37 1 11 an an DET 4j03cz32m37 1 12 account account NOUN 4j03cz32m37 1 13 of of ADP 4j03cz32m37 1 14 absolute absolute ADJ 4j03cz32m37 1 15 provability provability NOUN 4j03cz32m37 1 16 as as SCONJ 4j03cz32m37 1 17 this this DET 4j03cz32m37 1 18 notion notion NOUN 4j03cz32m37 1 19 was be AUX 4j03cz32m37 1 20 understood understand VERB 4j03cz32m37 1 21 by by ADP 4j03cz32m37 1 22 gödel gödel SPACE 4j03cz32m37 1 23 , , PUNCT 4j03cz32m37 1 24 post post ADJ 4j03cz32m37 1 25 , , PUNCT 4j03cz32m37 1 26 tarski tarski ADJ 4j03cz32m37 1 27 , , PUNCT 4j03cz32m37 1 28 and and CCONJ 4j03cz32m37 1 29 other other ADJ 4j03cz32m37 1 30 twentieth twentieth ADJ 4j03cz32m37 1 31 century century NOUN 4j03cz32m37 1 32 logicians logician NOUN 4j03cz32m37 1 33 . . PUNCT 4j03cz32m37 2 1 in in ADP 4j03cz32m37 2 2 chapter chapter NOUN 4j03cz32m37 2 3 1 1 NUM 4j03cz32m37 2 4 , , PUNCT 4j03cz32m37 2 5 i i PRON 4j03cz32m37 2 6 consider consider VERB 4j03cz32m37 2 7 some some DET 4j03cz32m37 2 8 problems problem NOUN 4j03cz32m37 2 9 facing face VERB 4j03cz32m37 2 10 existing exist VERB 4j03cz32m37 2 11 accounts account NOUN 4j03cz32m37 2 12 of of ADP 4j03cz32m37 2 13 absolute absolute ADJ 4j03cz32m37 2 14 provability provability NOUN 4j03cz32m37 2 15 , , PUNCT 4j03cz32m37 2 16 accounts account NOUN 4j03cz32m37 2 17 which which PRON 4j03cz32m37 2 18 describe describe VERB 4j03cz32m37 2 19 this this DET 4j03cz32m37 2 20 notion notion NOUN 4j03cz32m37 2 21 as as ADP 4j03cz32m37 2 22 involving involve VERB 4j03cz32m37 2 23 an an DET 4j03cz32m37 2 24 idealization idealization NOUN 4j03cz32m37 2 25 from from ADP 4j03cz32m37 2 26 concrete concrete ADJ 4j03cz32m37 2 27 mathematical mathematical ADJ 4j03cz32m37 2 28 practice practice NOUN 4j03cz32m37 2 29 . . PUNCT 4j03cz32m37 3 1 i i PRON 4j03cz32m37 3 2 propose propose VERB 4j03cz32m37 3 3 an an DET 4j03cz32m37 3 4 alternative alternative ADJ 4j03cz32m37 3 5 & & CCONJ 4j03cz32m37 3 6 quot;top quot;top NOUN 4j03cz32m37 3 7 - - PUNCT 4j03cz32m37 3 8 down" down" PROPN 4j03cz32m37 3 9 ; ; PUNCT 4j03cz32m37 3 10 approach approach NOUN 4j03cz32m37 3 11 to to ADP 4j03cz32m37 3 12 absolute absolute ADJ 4j03cz32m37 3 13 provability provability NOUN 4j03cz32m37 3 14 , , PUNCT 4j03cz32m37 3 15 on on ADP 4j03cz32m37 3 16 which which PRON 4j03cz32m37 3 17 we we PRON 4j03cz32m37 3 18 devise devise VERB 4j03cz32m37 3 19 a a DET 4j03cz32m37 3 20 proof proof ADJ 4j03cz32m37 3 21 concept concept NOUN 4j03cz32m37 3 22 satisfying satisfy VERB 4j03cz32m37 3 23 certain certain ADJ 4j03cz32m37 3 24 essential essential ADJ 4j03cz32m37 3 25 properties property NOUN 4j03cz32m37 3 26 of of ADP 4j03cz32m37 3 27 proof proof NOUN 4j03cz32m37 3 28 . . PUNCT 4j03cz32m37 4 1 i i PRON 4j03cz32m37 4 2 describe describe VERB 4j03cz32m37 4 3 two two NUM 4j03cz32m37 4 4 such such ADJ 4j03cz32m37 4 5 properties property NOUN 4j03cz32m37 4 6 : : PUNCT 4j03cz32m37 4 7 the the DET 4j03cz32m37 4 8 subgroundedness subgroundedness ADJ 4j03cz32m37 4 9 requirement requirement NOUN 4j03cz32m37 4 10 , , PUNCT 4j03cz32m37 4 11 the the DET 4j03cz32m37 4 12 requirement requirement NOUN 4j03cz32m37 4 13 that that SCONJ 4j03cz32m37 4 14 one one PRON 4j03cz32m37 4 15 should should AUX 4j03cz32m37 4 16 not not PART 4j03cz32m37 4 17 adopt adopt VERB 4j03cz32m37 4 18 as as ADP 4j03cz32m37 4 19 absolute absolute ADJ 4j03cz32m37 4 20 a a DET 4j03cz32m37 4 21 method method NOUN 4j03cz32m37 4 22 of of ADP 4j03cz32m37 4 23 proof proof NOUN 4j03cz32m37 4 24 p p PROPN 4j03cz32m37 4 25 which which PRON 4j03cz32m37 4 26 admits admit VERB 4j03cz32m37 4 27 extensions extension NOUN 4j03cz32m37 4 28 by by ADP 4j03cz32m37 4 29 further further ADJ 4j03cz32m37 4 30 methods method NOUN 4j03cz32m37 4 31 that that PRON 4j03cz32m37 4 32 can can AUX 4j03cz32m37 4 33 be be AUX 4j03cz32m37 4 34 seen see VERB 4j03cz32m37 4 35 to to PART 4j03cz32m37 4 36 be be AUX 4j03cz32m37 4 37 correct correct ADJ 4j03cz32m37 4 38 on on ADP 4j03cz32m37 4 39 the the DET 4j03cz32m37 4 40 same same ADJ 4j03cz32m37 4 41 basis basis NOUN 4j03cz32m37 4 42 as as ADP 4j03cz32m37 4 43 p p PROPN 4j03cz32m37 4 44 ; ; PUNCT 4j03cz32m37 4 45 and and CCONJ 4j03cz32m37 4 46 the the DET 4j03cz32m37 4 47 axiom axiom NOUN 4j03cz32m37 4 48 of of ADP 4j03cz32m37 4 49 solvability solvability NOUN 4j03cz32m37 4 50 , , PUNCT 4j03cz32m37 4 51 the the DET 4j03cz32m37 4 52 axiom axiom NOUN 4j03cz32m37 4 53 that that SCONJ 4j03cz32m37 4 54 all all DET 4j03cz32m37 4 55 definite definite ADJ 4j03cz32m37 4 56 mathematical mathematical ADJ 4j03cz32m37 4 57 propositions proposition NOUN 4j03cz32m37 4 58 can can AUX 4j03cz32m37 4 59 either either CCONJ 4j03cz32m37 4 60 be be AUX 4j03cz32m37 4 61 proved prove VERB 4j03cz32m37 4 62 , , PUNCT 4j03cz32m37 4 63 refuted refute VERB 4j03cz32m37 4 64 , , PUNCT 4j03cz32m37 4 65 or or CCONJ 4j03cz32m37 4 66 proved prove VERB 4j03cz32m37 4 67 to to PART 4j03cz32m37 4 68 be be AUX 4j03cz32m37 4 69 undecidable undecidable ADJ 4j03cz32m37 4 70 . . PUNCT 4j03cz32m37 5 1 in in ADP 4j03cz32m37 5 2 chapter chapter NOUN 4j03cz32m37 5 3 2 2 NUM 4j03cz32m37 5 4 , , PUNCT 4j03cz32m37 5 5 i i PRON 4j03cz32m37 5 6 describe describe VERB 4j03cz32m37 5 7 and and CCONJ 4j03cz32m37 5 8 contrast contrast VERB 4j03cz32m37 5 9 post post NOUN 4j03cz32m37 5 10 and and CCONJ 4j03cz32m37 5 11 gödel gödel SPACE 4j03cz32m37 5 12 's 's PART 4j03cz32m37 5 13 respective respective ADJ 4j03cz32m37 5 14 conceptions conception NOUN 4j03cz32m37 5 15 of of ADP 4j03cz32m37 5 16 absolute absolute ADJ 4j03cz32m37 5 17 provability provability NOUN 4j03cz32m37 5 18 . . PUNCT 4j03cz32m37 6 1 i i PRON 4j03cz32m37 6 2 argue argue VERB 4j03cz32m37 6 3 that that SCONJ 4j03cz32m37 6 4 the the DET 4j03cz32m37 6 5 common common ADJ 4j03cz32m37 6 6 features feature NOUN 4j03cz32m37 6 7 of of ADP 4j03cz32m37 6 8 their their PRON 4j03cz32m37 6 9 conceptions conception NOUN 4j03cz32m37 6 10 reflect reflect VERB 4j03cz32m37 6 11 a a DET 4j03cz32m37 6 12 shared share VERB 4j03cz32m37 6 13 adherence adherence NOUN 4j03cz32m37 6 14 to to ADP 4j03cz32m37 6 15 the the DET 4j03cz32m37 6 16 subgroundedness subgroundedness ADJ 4j03cz32m37 6 17 requirement requirement NOUN 4j03cz32m37 6 18 as as ADP 4j03cz32m37 6 19 an an DET 4j03cz32m37 6 20 essential essential ADJ 4j03cz32m37 6 21 property property NOUN 4j03cz32m37 6 22 of of ADP 4j03cz32m37 6 23 proof proof NOUN 4j03cz32m37 6 24 . . PUNCT 4j03cz32m37 7 1 in in ADP 4j03cz32m37 7 2 chapter chapter NOUN 4j03cz32m37 7 3 3 3 NUM 4j03cz32m37 7 4 , , PUNCT 4j03cz32m37 7 5 i i PRON 4j03cz32m37 7 6 describe describe VERB 4j03cz32m37 7 7 another another DET 4j03cz32m37 7 8 family family NOUN 4j03cz32m37 7 9 of of ADP 4j03cz32m37 7 10 conceptions conception NOUN 4j03cz32m37 7 11 of of ADP 4j03cz32m37 7 12 absolute absolute ADJ 4j03cz32m37 7 13 provability provability NOUN 4j03cz32m37 7 14 which which PRON 4j03cz32m37 7 15 includes include VERB 4j03cz32m37 7 16 the the DET 4j03cz32m37 7 17 conceptions conception NOUN 4j03cz32m37 7 18 of of ADP 4j03cz32m37 7 19 cohen cohen PROPN 4j03cz32m37 7 20 , , PUNCT 4j03cz32m37 7 21 mostowski mostowski PROPN 4j03cz32m37 7 22 , , PUNCT 4j03cz32m37 7 23 and and CCONJ 4j03cz32m37 7 24 hamkins hamkin NOUN 4j03cz32m37 7 25 . . PUNCT 4j03cz32m37 8 1 on on ADP 4j03cz32m37 8 2 these these PRON 4j03cz32m37 8 3 & & CCONJ 4j03cz32m37 8 4 quot;limitative" quot;limitative" PROPN 4j03cz32m37 8 5 ; ; PUNCT 4j03cz32m37 8 6 accounts account NOUN 4j03cz32m37 8 7 , , PUNCT 4j03cz32m37 8 8 absolute absolute ADJ 4j03cz32m37 8 9 provability provability NOUN 4j03cz32m37 8 10 serves serve VERB 4j03cz32m37 8 11 to to PART 4j03cz32m37 8 12 close close VERB 4j03cz32m37 8 13 research research NOUN 4j03cz32m37 8 14 problems problem NOUN 4j03cz32m37 8 15 which which PRON 4j03cz32m37 8 16 can can AUX 4j03cz32m37 8 17 be be AUX 4j03cz32m37 8 18 compellingly compellingly ADV 4j03cz32m37 8 19 argued argue VERB 4j03cz32m37 8 20 to to PART 4j03cz32m37 8 21 be be AUX 4j03cz32m37 8 22 absolutely absolutely ADV 4j03cz32m37 8 23 undecidable undecidable ADJ 4j03cz32m37 8 24 . . PUNCT 4j03cz32m37 9 1 the the DET 4j03cz32m37 9 2 inclination inclination NOUN 4j03cz32m37 9 3 to to PART 4j03cz32m37 9 4 settle settle VERB 4j03cz32m37 9 5 problems problem NOUN 4j03cz32m37 9 6 in in ADP 4j03cz32m37 9 7 this this DET 4j03cz32m37 9 8 way way NOUN 4j03cz32m37 9 9 , , PUNCT 4j03cz32m37 9 10 i i PRON 4j03cz32m37 9 11 argue argue VERB 4j03cz32m37 9 12 , , PUNCT 4j03cz32m37 9 13 reflects reflect VERB 4j03cz32m37 9 14 an an DET 4j03cz32m37 9 15 implicit implicit ADJ 4j03cz32m37 9 16 adherence adherence NOUN 4j03cz32m37 9 17 to to ADP 4j03cz32m37 9 18 the the DET 4j03cz32m37 9 19 axiom axiom NOUN 4j03cz32m37 9 20 of of ADP 4j03cz32m37 9 21 solvability solvability NOUN 4j03cz32m37 9 22 . . PUNCT 4j03cz32m37 10 1 in in ADP 4j03cz32m37 10 2 chapter chapter NOUN 4j03cz32m37 10 3 4 4 NUM 4j03cz32m37 10 4 , , PUNCT 4j03cz32m37 10 5 i i PRON 4j03cz32m37 10 6 develop develop VERB 4j03cz32m37 10 7 a a DET 4j03cz32m37 10 8 formal formal ADJ 4j03cz32m37 10 9 framework framework NOUN 4j03cz32m37 10 10 for for ADP 4j03cz32m37 10 11 representing represent VERB 4j03cz32m37 10 12 a a DET 4j03cz32m37 10 13 proof proof NOUN 4j03cz32m37 10 14 - - PUNCT 4j03cz32m37 10 15 concept concept NOUN 4j03cz32m37 10 16 satisfying satisfy VERB 4j03cz32m37 10 17 the the DET 4j03cz32m37 10 18 two two NUM 4j03cz32m37 10 19 essential essential ADJ 4j03cz32m37 10 20 properties property NOUN 4j03cz32m37 10 21 described describe VERB 4j03cz32m37 10 22 in in ADP 4j03cz32m37 10 23 chapter chapter NOUN 4j03cz32m37 10 24 one one NUM 4j03cz32m37 10 25 . . PUNCT 4j03cz32m37 11 1 i i PRON 4j03cz32m37 11 2 use use VERB 4j03cz32m37 11 3 this this DET 4j03cz32m37 11 4 framework framework NOUN 4j03cz32m37 11 5 to to PART 4j03cz32m37 11 6 argue argue VERB 4j03cz32m37 11 7 that that SCONJ 4j03cz32m37 11 8 absolute absolute ADJ 4j03cz32m37 11 9 provability provability NOUN 4j03cz32m37 11 10 is be AUX 4j03cz32m37 11 11 in in ADP 4j03cz32m37 11 12 a a DET 4j03cz32m37 11 13 certain certain ADJ 4j03cz32m37 11 14 sense sense NOUN 4j03cz32m37 11 15 ineffable ineffable ADJ 4j03cz32m37 11 16 , , PUNCT 4j03cz32m37 11 17 but but CCONJ 4j03cz32m37 11 18 that that SCONJ 4j03cz32m37 11 19 it it PRON 4j03cz32m37 11 20 is be AUX 4j03cz32m37 11 21 nevertheless nevertheless ADV 4j03cz32m37 11 22 amenable amenable ADJ 4j03cz32m37 11 23 to to PART 4j03cz32m37 11 24 study study VERB 4j03cz32m37 11 25 by by ADP 4j03cz32m37 11 26 formal formal ADJ 4j03cz32m37 11 27 methods method NOUN 4j03cz32m37 11 28 . . PUNCT 4j03cz32m37 12 1 in in ADP 4j03cz32m37 12 2 the the DET 4j03cz32m37 12 3 mathematical mathematical ADJ 4j03cz32m37 12 4 part part NOUN 4j03cz32m37 12 5 of of ADP 4j03cz32m37 12 6 the the DET 4j03cz32m37 12 7 dissertation dissertation NOUN 4j03cz32m37 12 8 , , PUNCT 4j03cz32m37 12 9 i i PRON 4j03cz32m37 12 10 define define VERB 4j03cz32m37 12 11 and and CCONJ 4j03cz32m37 12 12 study study VERB 4j03cz32m37 12 13 the the DET 4j03cz32m37 12 14 provability provability NOUN 4j03cz32m37 12 15 logics logic NOUN 4j03cz32m37 12 16 associated associate VERB 4j03cz32m37 12 17 with with ADP 4j03cz32m37 12 18 woodin woodin PROPN 4j03cz32m37 12 19 's 's PART 4j03cz32m37 12 20 notions notion NOUN 4j03cz32m37 12 21 of of ADP 4j03cz32m37 12 22 & & CCONJ 4j03cz32m37 12 23 # # SYM 4j03cz32m37 12 24 937;-consequence 937;-consequence NUM 4j03cz32m37 12 25 and and CCONJ 4j03cz32m37 12 26 & & CCONJ 4j03cz32m37 12 27 # # SYM 4j03cz32m37 12 28 937;-provability 937;-provability NUM 4j03cz32m37 12 29 . . PUNCT 4j03cz32m37 13 1 i i PRON 4j03cz32m37 13 2 demonstrate demonstrate VERB 4j03cz32m37 13 3 that that SCONJ 4j03cz32m37 13 4 most most ADJ 4j03cz32m37 13 5 of of ADP 4j03cz32m37 13 6 these these DET 4j03cz32m37 13 7 logics logic NOUN 4j03cz32m37 13 8 contain contain VERB 4j03cz32m37 13 9 gl gl NOUN 4j03cz32m37 13 10 , , PUNCT 4j03cz32m37 13 11 and and CCONJ 4j03cz32m37 13 12 i i PRON 4j03cz32m37 13 13 give give VERB 4j03cz32m37 13 14 upper upper ADJ 4j03cz32m37 13 15 and and CCONJ 4j03cz32m37 13 16 lower low ADJ 4j03cz32m37 13 17 bounds bound NOUN 4j03cz32m37 13 18 for for ADP 4j03cz32m37 13 19 a a DET 4j03cz32m37 13 20 number number NOUN 4j03cz32m37 13 21 of of ADP 4j03cz32m37 13 22 such such ADJ 4j03cz32m37 13 23 logics logic NOUN 4j03cz32m37 13 24 . . PUNCT 4j03cz32m37 14 1 in in ADP 4j03cz32m37 14 2 particular particular ADJ 4j03cz32m37 14 3 , , PUNCT 4j03cz32m37 14 4 in in ADP 4j03cz32m37 14 5 a a DET 4j03cz32m37 14 6 certain certain ADJ 4j03cz32m37 14 7 metatheory metatheory NOUN 4j03cz32m37 14 8 w w ADP 4j03cz32m37 14 9 , , PUNCT 4j03cz32m37 14 10 the the DET 4j03cz32m37 14 11 provability provability NOUN 4j03cz32m37 14 12 logic logic NOUN 4j03cz32m37 14 13 of of ADP 4j03cz32m37 14 14 & & CCONJ 4j03cz32m37 14 15 # # SYM 4j03cz32m37 14 16 937;-consequence 937;-consequence NUM 4j03cz32m37 14 17 from from ADP 4j03cz32m37 14 18 w w PROPN 4j03cz32m37 14 19 is be AUX 4j03cz32m37 14 20 precisely precisely ADV 4j03cz32m37 14 21 gl gl NOUN 4j03cz32m37 14 22 . . PUNCT