id sid tid token lemma pos ns064457k8r 1 1 using use VERB ns064457k8r 1 2 classical classical ADJ ns064457k8r 1 3 definitions definition NOUN ns064457k8r 1 4 from from ADP ns064457k8r 1 5 admissible admissible ADJ ns064457k8r 1 6 set set NOUN ns064457k8r 1 7 theory theory NOUN ns064457k8r 1 8 , , PUNCT ns064457k8r 1 9 we we PRON ns064457k8r 1 10 examine examine VERB ns064457k8r 1 11 computable computable ADJ ns064457k8r 1 12 model model NOUN ns064457k8r 1 13 theory theory NOUN ns064457k8r 1 14 for for ADP ns064457k8r 1 15 uncountable uncountable ADJ ns064457k8r 1 16 structures structure NOUN ns064457k8r 1 17 . . PUNCT ns064457k8r 2 1 we we PRON ns064457k8r 2 2 begin begin VERB ns064457k8r 2 3 the the DET ns064457k8r 2 4 first first ADJ ns064457k8r 2 5 chapter chapter NOUN ns064457k8r 2 6 by by ADP ns064457k8r 2 7 recalling recall VERB ns064457k8r 2 8 several several ADJ ns064457k8r 2 9 classic classic ADJ ns064457k8r 2 10 results result NOUN ns064457k8r 2 11 from from ADP ns064457k8r 2 12 & & CCONJ ns064457k8r 2 13 # # SYM ns064457k8r 2 14 945;-recursion 945;-recursion NUM ns064457k8r 2 15 , , PUNCT ns064457k8r 2 16 as as SCONJ ns064457k8r 2 17 stated state VERB ns064457k8r 2 18 in in ADP ns064457k8r 2 19 greenberg greenberg PROPN ns064457k8r 2 20 and and CCONJ ns064457k8r 2 21 knight knight NOUN ns064457k8r 2 22 . . PUNCT ns064457k8r 3 1 we we PRON ns064457k8r 3 2 give give VERB ns064457k8r 3 3 a a DET ns064457k8r 3 4 few few ADJ ns064457k8r 3 5 examples example NOUN ns064457k8r 3 6 of of ADP ns064457k8r 3 7 ' ' PUNCT ns064457k8r 3 8 & & CCONJ ns064457k8r 3 9 # # SYM ns064457k8r 3 10 969;2 969;2 NUM ns064457k8r 3 11 - - PUNCT ns064457k8r 3 12 computable computable NOUN ns064457k8r 3 13 ' ' PART ns064457k8r 3 14 structures structure NOUN ns064457k8r 3 15 . . PUNCT ns064457k8r 4 1 in in ADP ns064457k8r 4 2 the the DET ns064457k8r 4 3 second second ADJ ns064457k8r 4 4 chapter chapter NOUN ns064457k8r 4 5 , , PUNCT ns064457k8r 4 6 we we PRON ns064457k8r 4 7 continue continue VERB ns064457k8r 4 8 work work NOUN ns064457k8r 4 9 of of ADP ns064457k8r 4 10 greenberg greenberg PROPN ns064457k8r 4 11 and and CCONJ ns064457k8r 4 12 knight knight NOUN ns064457k8r 4 13 on on ADP ns064457k8r 4 14 ' ' PUNCT ns064457k8r 4 15 & & CCONJ ns064457k8r 4 16 # # SYM ns064457k8r 4 17 969;2 969;2 NUM ns064457k8r 4 18 - - PUNCT ns064457k8r 4 19 computable computable NOUN ns064457k8r 4 20 ' ' PUNCT ns064457k8r 4 21 structure structure NOUN ns064457k8r 4 22 theory theory NOUN ns064457k8r 4 23 . . PUNCT ns064457k8r 5 1 all all DET ns064457k8r 5 2 results result NOUN ns064457k8r 5 3 in in ADP ns064457k8r 5 4 this this DET ns064457k8r 5 5 chapter chapter NOUN ns064457k8r 5 6 are be AUX ns064457k8r 5 7 joint joint ADJ ns064457k8r 5 8 with with ADP ns064457k8r 5 9 jacob jacob PROPN ns064457k8r 5 10 carson carson PROPN ns064457k8r 5 11 , , PUNCT ns064457k8r 5 12 julia julia PROPN ns064457k8r 5 13 knight knight PROPN ns064457k8r 5 14 , , PUNCT ns064457k8r 5 15 karen karen PROPN ns064457k8r 5 16 lange lange PROPN ns064457k8r 5 17 , , PUNCT ns064457k8r 5 18 charles charles PROPN ns064457k8r 5 19 mccoy mccoy PROPN ns064457k8r 5 20 , , PUNCT ns064457k8r 5 21 and and CCONJ ns064457k8r 5 22 john john PROPN ns064457k8r 5 23 wallbaum wallbaum PROPN ns064457k8r 5 24 . . PUNCT ns064457k8r 6 1 we we PRON ns064457k8r 6 2 define define VERB ns064457k8r 6 3 the the DET ns064457k8r 6 4 arithmetical arithmetical ADJ ns064457k8r 6 5 hierarchy hierarchy NOUN ns064457k8r 6 6 through through ADP ns064457k8r 6 7 all all DET ns064457k8r 6 8 countable countable ADJ ns064457k8r 6 9 levels level NOUN ns064457k8r 6 10 ( ( PUNCT ns064457k8r 6 11 not not PART ns064457k8r 6 12 just just ADV ns064457k8r 6 13 finite finite ADJ ns064457k8r 6 14 levels level NOUN ns064457k8r 6 15 ) ) PUNCT ns064457k8r 6 16 . . PUNCT ns064457k8r 7 1 the the DET ns064457k8r 7 2 definition definition NOUN ns064457k8r 7 3 resembles resemble VERB ns064457k8r 7 4 that that PRON ns064457k8r 7 5 of of ADP ns064457k8r 7 6 the the DET ns064457k8r 7 7 hyperarithmetical hyperarithmetical ADJ ns064457k8r 7 8 hierarchy hierarchy NOUN ns064457k8r 7 9 . . PUNCT ns064457k8r 8 1 we we PRON ns064457k8r 8 2 obtain obtain VERB ns064457k8r 8 3 analogues analogue NOUN ns064457k8r 8 4 of of ADP ns064457k8r 8 5 the the DET ns064457k8r 8 6 results result NOUN ns064457k8r 8 7 of of ADP ns064457k8r 8 8 chisholm chisholm PROPN ns064457k8r 8 9 and and CCONJ ns064457k8r 8 10 ash ash PROPN ns064457k8r 8 11 , , PUNCT ns064457k8r 8 12 knight knight NOUN ns064457k8r 8 13 , , PUNCT ns064457k8r 8 14 manasse manasse ADJ ns064457k8r 8 15 , , PUNCT ns064457k8r 8 16 and and CCONJ ns064457k8r 8 17 slaman slaman NOUN ns064457k8r 8 18 , , PUNCT ns064457k8r 8 19 saying say VERB ns064457k8r 8 20 that that SCONJ ns064457k8r 8 21 a a DET ns064457k8r 8 22 relation relation NOUN ns064457k8r 8 23 is be AUX ns064457k8r 8 24 relatively relatively ADV ns064457k8r 8 25 intrinsically intrinsically ADV ns064457k8r 8 26 & & CCONJ ns064457k8r 8 27 # # SYM ns064457k8r 8 28 931;0α 931;0α NUM ns064457k8r 8 29 ; ; PUNCT ns064457k8r 8 30 if if SCONJ ns064457k8r 8 31 and and CCONJ ns064457k8r 8 32 only only ADV ns064457k8r 8 33 if if SCONJ ns064457k8r 8 34 it it PRON ns064457k8r 8 35 is be AUX ns064457k8r 8 36 definable definable ADJ ns064457k8r 8 37 by by ADP ns064457k8r 8 38 a a DET ns064457k8r 8 39 computable computable NOUN ns064457k8r 8 40 & & CCONJ ns064457k8r 8 41 # # SYM ns064457k8r 8 42 931;α 931;α NUM ns064457k8r 8 43 ; ; PUNCT ns064457k8r 8 44 formula formula NOUN ns064457k8r 8 45 . . PUNCT ns064457k8r 9 1 in in ADP ns064457k8r 9 2 the the DET ns064457k8r 9 3 third third ADJ ns064457k8r 9 4 chapter chapter NOUN ns064457k8r 9 5 , , PUNCT ns064457k8r 9 6 we we PRON ns064457k8r 9 7 focus focus VERB ns064457k8r 9 8 on on ADP ns064457k8r 9 9 quasiminimal quasiminimal ADJ ns064457k8r 9 10 - - PUNCT ns064457k8r 9 11 excellent excellent ADJ ns064457k8r 9 12 classes class NOUN ns064457k8r 9 13 , , PUNCT ns064457k8r 9 14 which which PRON ns064457k8r 9 15 are be AUX ns064457k8r 9 16 important important ADJ ns064457k8r 9 17 classes class NOUN ns064457k8r 9 18 of of ADP ns064457k8r 9 19 structures structure NOUN ns064457k8r 9 20 in in ADP ns064457k8r 9 21 modern modern ADJ ns064457k8r 9 22 model model NOUN ns064457k8r 9 23 theory theory NOUN ns064457k8r 9 24 . . PUNCT ns064457k8r 10 1 we we PRON ns064457k8r 10 2 give give VERB ns064457k8r 10 3 a a DET ns064457k8r 10 4 definition definition NOUN ns064457k8r 10 5 for for ADP ns064457k8r 10 6 & & CCONJ ns064457k8r 10 7 # # SYM ns064457k8r 10 8 954;+-computable 954;+-computable NUM ns064457k8r 10 9 categoricity categoricity NOUN ns064457k8r 10 10 and and CCONJ ns064457k8r 10 11 give give VERB ns064457k8r 10 12 properties property NOUN ns064457k8r 10 13 of of ADP ns064457k8r 10 14 classes class NOUN ns064457k8r 10 15 of of ADP ns064457k8r 10 16 structures structure NOUN ns064457k8r 10 17 , , PUNCT ns064457k8r 10 18 under under ADP ns064457k8r 10 19 which which PRON ns064457k8r 10 20 the the DET ns064457k8r 10 21 unique unique ADJ ns064457k8r 10 22 element element NOUN ns064457k8r 10 23 of of ADP ns064457k8r 10 24 size size NOUN ns064457k8r 10 25 & & CCONJ ns064457k8r 10 26 # # SYM ns064457k8r 10 27 954;+ 954;+ NUM ns064457k8r 10 28 has have VERB ns064457k8r 10 29 a a DET ns064457k8r 10 30 & & CCONJ ns064457k8r 10 31 # # SYM ns064457k8r 10 32 954;+-computable 954;+-computable NUM ns064457k8r 10 33 copy copy NOUN ns064457k8r 10 34 and and CCONJ ns064457k8r 10 35 is be AUX ns064457k8r 10 36 & & CCONJ ns064457k8r 10 37 # # SYM ns064457k8r 10 38 954;+-Δ02 954;+-Δ02 NUM ns064457k8r 10 39 - - PUNCT ns064457k8r 10 40 categorical categorical ADJ ns064457k8r 10 41 . . PUNCT ns064457k8r 11 1 we we PRON ns064457k8r 11 2 then then ADV ns064457k8r 11 3 show show VERB ns064457k8r 11 4 that that SCONJ ns064457k8r 11 5 any any DET ns064457k8r 11 6 class class NOUN ns064457k8r 11 7 satisfying satisfy VERB ns064457k8r 11 8 these these DET ns064457k8r 11 9 properties property NOUN ns064457k8r 11 10 is be AUX ns064457k8r 11 11 & & CCONJ ns064457k8r 11 12 # # SYM ns064457k8r 11 13 954;+-computably 954;+-computably NUM ns064457k8r 11 14 categorical categorical ADJ ns064457k8r 11 15 if if SCONJ ns064457k8r 11 16 and and CCONJ ns064457k8r 11 17 only only ADV ns064457k8r 11 18 if if SCONJ ns064457k8r 11 19 there there PRON ns064457k8r 11 20 is be VERB ns064457k8r 11 21 no no PRON ns064457k8r 11 22 triple triple ADJ ns064457k8r 11 23 ( ( PUNCT ns064457k8r 11 24 n',n n',n PROPN ns064457k8r 11 25 , , PUNCT ns064457k8r 11 26 m m PROPN ns064457k8r 11 27 ) ) PUNCT ns064457k8r 11 28 of of ADP ns064457k8r 11 29 structures structure NOUN ns064457k8r 11 30 of of ADP ns064457k8r 11 31 dimension dimension NOUN ns064457k8r 11 32 & & CCONJ ns064457k8r 11 33 # # SYM ns064457k8r 11 34 954 954 NUM ns064457k8r 11 35 ; ; PUNCT ns064457k8r 11 36 such such ADJ ns064457k8r 11 37 that that SCONJ ns064457k8r 11 38 m m PROPN ns064457k8r 11 39 & & CCONJ ns064457k8r 11 40 # # SYM ns064457k8r 11 41 8838 8838 NUM ns064457k8r 11 42 ; ; PUNCT ns064457k8r 11 43 n n NOUN ns064457k8r 11 44 & & CCONJ ns064457k8r 11 45 # # SYM ns064457k8r 11 46 8838 8838 NUM ns064457k8r 11 47 ; ; PUNCT ns064457k8r 11 48 n n CCONJ ns064457k8r 11 49 ' ' PUNCT ns064457k8r 11 50 and and CCONJ ns064457k8r 11 51 m m VERB ns064457k8r 11 52 is be AUX ns064457k8r 11 53 ' ' PUNCT ns064457k8r 11 54 closed closed ADJ ns064457k8r 11 55 ' ' PUNCT ns064457k8r 11 56 in in ADP ns064457k8r 11 57 n n NOUN ns064457k8r 11 58 and and CCONJ ns064457k8r 11 59 n n X ns064457k8r 11 60 ' ' PUNCT ns064457k8r 11 61 , , PUNCT ns064457k8r 11 62 but but CCONJ ns064457k8r 11 63 n n CCONJ ns064457k8r 11 64 is be AUX ns064457k8r 11 65 not not PART ns064457k8r 11 66 ' ' PUNCT ns064457k8r 11 67 closed close VERB ns064457k8r 11 68 ' ' PUNCT ns064457k8r 11 69 in in ADP ns064457k8r 11 70 n n NOUN ns064457k8r 11 71 ' ' PUNCT ns064457k8r 11 72 . . PUNCT ns064457k8r 12 1 we we PRON ns064457k8r 12 2 then then ADV ns064457k8r 12 3 apply apply VERB ns064457k8r 12 4 this this DET ns064457k8r 12 5 result result NOUN ns064457k8r 12 6 to to ADP ns064457k8r 12 7 some some DET ns064457k8r 12 8 well well ADV ns064457k8r 12 9 - - PUNCT ns064457k8r 12 10 known know VERB ns064457k8r 12 11 examples example NOUN ns064457k8r 12 12 of of ADP ns064457k8r 12 13 quasiminimal quasiminimal ADJ ns064457k8r 12 14 - - PUNCT ns064457k8r 12 15 excellent excellent NOUN ns064457k8r 12 16 classes class NOUN ns064457k8r 12 17 , , PUNCT ns064457k8r 12 18 showing show VERB ns064457k8r 12 19 that that SCONJ ns064457k8r 12 20 the the DET ns064457k8r 12 21 pseudo pseudo ADJ ns064457k8r 12 22 - - ADJ ns064457k8r 12 23 exponential exponential ADJ ns064457k8r 12 24 field field NOUN ns064457k8r 12 25 of of ADP ns064457k8r 12 26 size size NOUN ns064457k8r 12 27 & & CCONJ ns064457k8r 12 28 # # SYM ns064457k8r 12 29 954;+ 954;+ NUM ns064457k8r 12 30 is be AUX ns064457k8r 12 31 not not PART ns064457k8r 12 32 & & CCONJ ns064457k8r 12 33 # # SYM ns064457k8r 12 34 954;+-computably 954;+-computably NUM ns064457k8r 12 35 categorical categorical ADJ ns064457k8r 12 36 , , PUNCT ns064457k8r 12 37 but but CCONJ ns064457k8r 12 38 the the DET ns064457k8r 12 39 ' ' PUNCT ns064457k8r 12 40 zil'ber zil'ber PROPN ns064457k8r 12 41 cover cover NOUN ns064457k8r 12 42 ' ' PUNCT ns064457k8r 12 43 is be AUX ns064457k8r 12 44 relatively relatively ADV ns064457k8r 12 45 & & CCONJ ns064457k8r 12 46 # # SYM ns064457k8r 12 47 954;+-computably 954;+-computably NUM ns064457k8r 12 48 categorical categorical ADJ ns064457k8r 12 49 . . PUNCT ns064457k8r 13 1 we we PRON ns064457k8r 13 2 end end VERB ns064457k8r 13 3 by by ADP ns064457k8r 13 4 connecting connect VERB ns064457k8r 13 5 the the DET ns064457k8r 13 6 results result NOUN ns064457k8r 13 7 of of ADP ns064457k8r 13 8 computable computable ADJ ns064457k8r 13 9 categoricity categoricity NOUN ns064457k8r 13 10 to to PART ns064457k8r 13 11 axiomatizability axiomatizability NOUN ns064457k8r 13 12 for for ADP ns064457k8r 13 13 quasiminimal quasiminimal ADJ ns064457k8r 13 14 - - PUNCT ns064457k8r 13 15 excellent excellent ADJ ns064457k8r 13 16 classes class NOUN ns064457k8r 13 17 . . PUNCT