id sid tid token lemma pos zp38w952r6r 1 1 in in ADP zp38w952r6r 1 2 this this DET zp38w952r6r 1 3 thesis thesis NOUN zp38w952r6r 1 4 we we PRON zp38w952r6r 1 5 develop develop VERB zp38w952r6r 1 6 the the DET zp38w952r6r 1 7 analysis analysis NOUN zp38w952r6r 1 8 of of ADP zp38w952r6r 1 9 the the DET zp38w952r6r 1 10 structure structure NOUN zp38w952r6r 1 11 of of ADP zp38w952r6r 1 12 a a DET zp38w952r6r 1 13 model model NOUN zp38w952r6r 1 14 , , PUNCT zp38w952r6r 1 15 modulo modulo NOUN zp38w952r6r 1 16 the the DET zp38w952r6r 1 17 structure structure NOUN zp38w952r6r 1 18 induced induce VERB zp38w952r6r 1 19 by by ADP zp38w952r6r 1 20 a a DET zp38w952r6r 1 21 part part NOUN zp38w952r6r 1 22 of of ADP zp38w952r6r 1 23 the the DET zp38w952r6r 1 24 model model NOUN zp38w952r6r 1 25 interpreting interpret VERB zp38w952r6r 1 26 a a DET zp38w952r6r 1 27 predicate predicate NOUN zp38w952r6r 1 28 , , PUNCT zp38w952r6r 1 29 p. p. PROPN zp38w952r6r 1 30 we we PRON zp38w952r6r 1 31 develop develop VERB zp38w952r6r 1 32 the the DET zp38w952r6r 1 33 ' ' PUNCT zp38w952r6r 1 34 morley morley ADJ zp38w952r6r 1 35 rank rank NOUN zp38w952r6r 1 36 modulo modulo PROPN zp38w952r6r 1 37 a a DET zp38w952r6r 1 38 predicate predicate NOUN zp38w952r6r 1 39 ' ' PUNCT zp38w952r6r 1 40 , , PUNCT zp38w952r6r 1 41 pmr pmr PROPN zp38w952r6r 1 42 , , PUNCT zp38w952r6r 1 43 and and CCONJ zp38w952r6r 1 44 define define VERB zp38w952r6r 1 45 an an DET zp38w952r6r 1 46 independence independence NOUN zp38w952r6r 1 47 relation relation NOUN zp38w952r6r 1 48 based base VERB zp38w952r6r 1 49 on on ADP zp38w952r6r 1 50 this this DET zp38w952r6r 1 51 rank rank NOUN zp38w952r6r 1 52 . . PUNCT zp38w952r6r 2 1 we we PRON zp38w952r6r 2 2 analyze analyze VERB zp38w952r6r 2 3 this this DET zp38w952r6r 2 4 relation relation NOUN zp38w952r6r 2 5 in in ADP zp38w952r6r 2 6 a a DET zp38w952r6r 2 7 nice nice ADJ zp38w952r6r 2 8 setting setting NOUN zp38w952r6r 2 9 ( ( PUNCT zp38w952r6r 2 10 where where SCONJ zp38w952r6r 2 11 every every DET zp38w952r6r 2 12 formula formula NOUN zp38w952r6r 2 13 has have AUX zp38w952r6r 2 14 pmr pmr VERB zp38w952r6r 2 15 ) ) PUNCT zp38w952r6r 2 16 in in ADP zp38w952r6r 2 17 terms term NOUN zp38w952r6r 2 18 of of ADP zp38w952r6r 2 19 the the DET zp38w952r6r 2 20 eight eight NUM zp38w952r6r 2 21 axioms axiom NOUN zp38w952r6r 2 22 of of ADP zp38w952r6r 2 23 stability stability NOUN zp38w952r6r 2 24 theory theory NOUN zp38w952r6r 2 25 . . PUNCT zp38w952r6r 3 1 we we PRON zp38w952r6r 3 2 prove prove VERB zp38w952r6r 3 3 a a DET zp38w952r6r 3 4 dichotomy dichotomy NOUN zp38w952r6r 3 5 theorem theorem NOUN zp38w952r6r 3 6 classifying classify VERB zp38w952r6r 3 7 pmr pmr PROPN zp38w952r6r 3 8 - - PUNCT zp38w952r6r 3 9 minimal minimal ADJ zp38w952r6r 3 10 structures structure NOUN zp38w952r6r 3 11 and and CCONJ zp38w952r6r 3 12 a a DET zp38w952r6r 3 13 two two NUM zp38w952r6r 3 14 - - PUNCT zp38w952r6r 3 15 cardinal cardinal NOUN zp38w952r6r 3 16 result result NOUN zp38w952r6r 3 17 . . PUNCT zp38w952r6r 4 1 finally finally ADV zp38w952r6r 4 2 , , PUNCT zp38w952r6r 4 3 we we PRON zp38w952r6r 4 4 give give VERB zp38w952r6r 4 5 a a DET zp38w952r6r 4 6 classification classification NOUN zp38w952r6r 4 7 of of ADP zp38w952r6r 4 8 the the DET zp38w952r6r 4 9 norms norm NOUN zp38w952r6r 4 10 one one PRON zp38w952r6r 4 11 can can AUX zp38w952r6r 4 12 place place VERB zp38w952r6r 4 13 on on ADP zp38w952r6r 4 14 a a DET zp38w952r6r 4 15 finite finite ADJ zp38w952r6r 4 16 dimensional dimensional ADJ zp38w952r6r 4 17 vector vector NOUN zp38w952r6r 4 18 space space NOUN zp38w952r6r 4 19 over over ADP zp38w952r6r 4 20 the the DET zp38w952r6r 4 21 reals real NOUN zp38w952r6r 4 22 ( ( PUNCT zp38w952r6r 4 23 up up ADP zp38w952r6r 4 24 to to ADP zp38w952r6r 4 25 model model ADJ zp38w952r6r 4 26 - - PUNCT zp38w952r6r 4 27 theoretic theoretic ADJ zp38w952r6r 4 28 equivalence equivalence NOUN zp38w952r6r 4 29 ) ) PUNCT zp38w952r6r 4 30 . . PUNCT