id	sid	tid	token	lemma	pos
v979v12176z	1	1	the	the	DET
v979v12176z	1	2	class	class	NOUN
v979v12176z	1	3	of	of	ADP
v979v12176z	1	4	real	real	ADJ
v979v12176z	1	5	closed	closed	ADJ
v979v12176z	1	6	fields	field	NOUN
v979v12176z	1	7	(	(	PUNCT
v979v12176z	1	8	rcf	rcf	PROPN
v979v12176z	1	9	)	)	PUNCT
v979v12176z	1	10	has	have	VERB
v979v12176z	1	11	nice	nice	ADJ
v979v12176z	1	12	model	model	NOUN
v979v12176z	1	13	theoretic	theoretic	ADJ
v979v12176z	1	14	properties	property	NOUN
v979v12176z	1	15	,	,	PUNCT
v979v12176z	1	16	among	among	ADP
v979v12176z	1	17	them	they	PRON
v979v12176z	1	18	o	o	NOUN
v979v12176z	1	19	-	-	NOUN
v979v12176z	1	20	minimality	minimality	NOUN
v979v12176z	1	21	and	and	CCONJ
v979v12176z	1	22	quantifier	quantifier	NOUN
v979v12176z	1	23	elimination	elimination	NOUN
v979v12176z	1	24	.	.	PUNCT
v979v12176z	2	1	we	we	PRON
v979v12176z	2	2	examine	examine	VERB
v979v12176z	2	3	rcf	rcf	PROPN
v979v12176z	2	4	and	and	CCONJ
v979v12176z	2	5	the	the	DET
v979v12176z	2	6	non	non	ADJ
v979v12176z	2	7	-	-	ADJ
v979v12176z	2	8	elementary	elementary	ADJ
v979v12176z	2	9	subclass	subclass	NOUN
v979v12176z	2	10	of	of	ADP
v979v12176z	2	11	rcf	rcf	PROPN
v979v12176z	2	12	composed	compose	VERB
v979v12176z	2	13	of	of	ADP
v979v12176z	2	14	archimedean	archimedean	ADJ
v979v12176z	2	15	real	real	ADJ
v979v12176z	2	16	closed	closed	ADJ
v979v12176z	2	17	fields	field	NOUN
v979v12176z	2	18	,	,	PUNCT
v979v12176z	2	19	arcf	arcf	ADV
v979v12176z	2	20	,	,	PUNCT
v979v12176z	2	21	from	from	ADP
v979v12176z	2	22	a	a	DET
v979v12176z	2	23	computable	computable	ADJ
v979v12176z	2	24	structure	structure	NOUN
v979v12176z	2	25	theory	theory	NOUN
v979v12176z	2	26	perspective	perspective	NOUN
v979v12176z	2	27	.	.	PUNCT
v979v12176z	3	1	also	also	ADV
v979v12176z	3	2	,	,	PUNCT
v979v12176z	3	3	we	we	PRON
v979v12176z	3	4	explore	explore	VERB
v979v12176z	3	5	connections	connection	NOUN
v979v12176z	3	6	with	with	ADP
v979v12176z	3	7	the	the	DET
v979v12176z	3	8	class	class	NOUN
v979v12176z	3	9	of	of	ADP
v979v12176z	3	10	linear	linear	ADJ
v979v12176z	3	11	orders	order	NOUN
v979v12176z	3	12	(	(	PUNCT
v979v12176z	3	13	lo	lo	INTJ
v979v12176z	3	14	)	)	PUNCT
v979v12176z	3	15	.	.	PUNCT
v979v12176z	4	1	we	we	PRON
v979v12176z	4	2	focus	focus	VERB
v979v12176z	4	3	on	on	ADP
v979v12176z	4	4	two	two	NUM
v979v12176z	4	5	main	main	ADJ
v979v12176z	4	6	notions	notion	NOUN
v979v12176z	4	7	:	:	PUNCT
v979v12176z	4	8	turing	ture	VERB
v979v12176z	4	9	computable	computable	ADJ
v979v12176z	4	10	embeddings	embedding	NOUN
v979v12176z	4	11	and	and	CCONJ
v979v12176z	4	12	relative	relative	ADJ
v979v12176z	4	13	categoricity.the	categoricity.the	DET
v979v12176z	4	14	notion	notion	NOUN
v979v12176z	4	15	of	of	ADP
v979v12176z	4	16	turing	ture	VERB
v979v12176z	4	17	computable	computable	NOUN
v979v12176z	4	18	embedding	embedding	NOUN
v979v12176z	4	19	(	(	PUNCT
v979v12176z	4	20	tce	tce	PROPN
v979v12176z	4	21	)	)	PUNCT
v979v12176z	4	22	is	be	AUX
v979v12176z	4	23	an	an	DET
v979v12176z	4	24	effective	effective	ADJ
v979v12176z	4	25	version	version	NOUN
v979v12176z	4	26	of	of	ADP
v979v12176z	4	27	the	the	DET
v979v12176z	4	28	borel	borel	PROPN
v979v12176z	4	29	embedding	embedding	NOUN
v979v12176z	4	30	defined	define	VERB
v979v12176z	4	31	by	by	ADP
v979v12176z	4	32	friedman	friedman	PROPN
v979v12176z	4	33	and	and	CCONJ
v979v12176z	4	34	stanley	stanley	PROPN
v979v12176z	4	35	in	in	ADP
v979v12176z	4	36	1989	1989	NUM
v979v12176z	5	1	[	[	X
v979v12176z	5	2	1	1	NUM
v979v12176z	5	3	]	]	PUNCT
v979v12176z	5	4	.	.	PUNCT
v979v12176z	6	1	in	in	ADP
v979v12176z	6	2	fact	fact	NOUN
v979v12176z	6	3	,	,	PUNCT
v979v12176z	6	4	many	many	ADJ
v979v12176z	6	5	borel	borel	ADJ
v979v12176z	6	6	embeddings	embedding	NOUN
v979v12176z	6	7	are	be	AUX
v979v12176z	6	8	computable	computable	ADJ
v979v12176z	6	9	.	.	PUNCT
v979v12176z	7	1	the	the	DET
v979v12176z	7	2	relation	relation	NOUN
v979v12176z	7	3	<	<	X
v979v12176z	7	4	is	be	AUX
v979v12176z	7	5	a	a	DET
v979v12176z	7	6	preordering	preordering	NOUN
v979v12176z	7	7	on	on	ADP
v979v12176z	7	8	classes	class	NOUN
v979v12176z	7	9	of	of	ADP
v979v12176z	7	10	structures	structure	NOUN
v979v12176z	7	11	.	.	PUNCT
v979v12176z	8	1	in	in	ADP
v979v12176z	8	2	[	[	X
v979v12176z	8	3	1	1	NUM
v979v12176z	8	4	]	]	PUNCT
v979v12176z	8	5	,	,	PUNCT
v979v12176z	8	6	the	the	DET
v979v12176z	8	7	authors	author	NOUN
v979v12176z	8	8	provide	provide	VERB
v979v12176z	8	9	a	a	DET
v979v12176z	8	10	computable	computable	ADJ
v979v12176z	8	11	borel	borel	NOUN
v979v12176z	8	12	reduction	reduction	NOUN
v979v12176z	8	13	showing	show	VERB
v979v12176z	8	14	that	that	SCONJ
v979v12176z	8	15	lo	lo	PROPN
v979v12176z	8	16	is	be	AUX
v979v12176z	8	17	a	a	DET
v979v12176z	8	18	maximal	maximal	ADJ
v979v12176z	8	19	element	element	NOUN
v979v12176z	8	20	of	of	ADP
v979v12176z	8	21	the	the	DET
v979v12176z	8	22	preordering	preordering	NOUN
v979v12176z	8	23	defined	define	VERB
v979v12176z	8	24	by	by	ADP
v979v12176z	8	25	tce	tce	PROPN
v979v12176z	8	26	's	's	PART
v979v12176z	8	27	.	.	PUNCT
v979v12176z	9	1	an	an	DET
v979v12176z	9	2	embedding	embedding	NOUN
v979v12176z	9	3	,	,	PUNCT
v979v12176z	9	4	due	due	ADP
v979v12176z	9	5	to	to	ADP
v979v12176z	9	6	marker	marker	NOUN
v979v12176z	9	7	and	and	CCONJ
v979v12176z	9	8	discussed	discuss	VERB
v979v12176z	9	9	by	by	ADP
v979v12176z	9	10	levin	levin	PROPN
v979v12176z	9	11	in	in	ADP
v979v12176z	9	12	his	his	PRON
v979v12176z	9	13	thesis	thesis	NOUN
v979v12176z	9	14	,	,	PUNCT
v979v12176z	9	15	shows	show	VERB
v979v12176z	9	16	that	that	SCONJ
v979v12176z	9	17	lo	lo	PROPN
v979v12176z	9	18	<	<	X
v979v12176z	9	19	rcf	rcf	PROPN
v979v12176z	9	20	,	,	PUNCT
v979v12176z	9	21	hence	hence	ADV
v979v12176z	9	22	rcf	rcf	ADV
v979v12176z	9	23	is	be	AUX
v979v12176z	9	24	also	also	ADV
v979v12176z	9	25	maximal.we	maximal.we	X
v979v12176z	9	26	consider	consider	VERB
v979v12176z	9	27	the	the	DET
v979v12176z	9	28	class	class	NOUN
v979v12176z	9	29	dg	dg	NOUN
v979v12176z	9	30	,	,	PUNCT
v979v12176z	9	31	of	of	ADP
v979v12176z	9	32	daisy	daisy	NOUN
v979v12176z	9	33	graphs	graph	NOUN
v979v12176z	9	34	,	,	PUNCT
v979v12176z	9	35	a	a	DET
v979v12176z	9	36	non	non	ADJ
v979v12176z	9	37	-	-	ADJ
v979v12176z	9	38	elementary	elementary	ADJ
v979v12176z	9	39	subclass	subclass	NOUN
v979v12176z	9	40	of	of	ADP
v979v12176z	9	41	the	the	DET
v979v12176z	9	42	class	class	NOUN
v979v12176z	9	43	of	of	ADP
v979v12176z	9	44	undirected	undirected	ADJ
v979v12176z	9	45	graphs	graph	NOUN
v979v12176z	9	46	.	.	PUNCT
v979v12176z	10	1	each	each	DET
v979v12176z	10	2	structure	structure	NOUN
v979v12176z	10	3	a	a	PRON
v979v12176z	10	4	in	in	ADP
v979v12176z	10	5	dg	dg	PROPN
v979v12176z	10	6	codes	code	VERB
v979v12176z	10	7	a	a	DET
v979v12176z	10	8	family	family	NOUN
v979v12176z	10	9	s	s	VERB
v979v12176z	10	10	of	of	ADP
v979v12176z	10	11	subsets	subset	NOUN
v979v12176z	10	12	of	of	ADP
v979v12176z	10	13	the	the	DET
v979v12176z	10	14	natural	natural	ADJ
v979v12176z	10	15	numbers	number	NOUN
v979v12176z	10	16	n.	n.	INTJ
v979v12176z	11	1	we	we	PRON
v979v12176z	11	2	show	show	VERB
v979v12176z	11	3	that	that	SCONJ
v979v12176z	11	4	each	each	PRON
v979v12176z	11	5	of	of	ADP
v979v12176z	11	6	dg	dg	PROPN
v979v12176z	11	7	and	and	CCONJ
v979v12176z	11	8	arcf	arcf	ADP
v979v12176z	11	9	is	be	AUX
v979v12176z	11	10	tc	tc	NOUN
v979v12176z	11	11	embeddable	embeddable	ADJ
v979v12176z	11	12	into	into	ADP
v979v12176z	11	13	the	the	DET
v979v12176z	11	14	other	other	ADJ
v979v12176z	11	15	.	.	PUNCT
v979v12176z	12	1	we	we	PRON
v979v12176z	12	2	use	use	VERB
v979v12176z	12	3	=	=	PUNCT
v979v12176z	12	4	to	to	PART
v979v12176z	12	5	denote	denote	VERB
v979v12176z	12	6	this.theorem	this.theorem	PROPN
v979v12176z	12	7	1	1	NUM
v979v12176z	12	8	:	:	PUNCT
v979v12176z	12	9	dg	dg	PROPN
v979v12176z	12	10	=	=	X
v979v12176z	12	11	arcf.to	arcf.to	X
v979v12176z	12	12	prove	prove	VERB
v979v12176z	12	13	theorem	theorem	NOUN
v979v12176z	12	14	1	1	NUM
v979v12176z	13	1	we	we	PRON
v979v12176z	13	2	construct	construct	VERB
v979v12176z	13	3	a	a	DET
v979v12176z	13	4	computable	computable	ADJ
v979v12176z	13	5	perfect	perfect	ADJ
v979v12176z	13	6	tree	tree	NOUN
v979v12176z	13	7	t	t	PROPN
v979v12176z	13	8	whose	whose	DET
v979v12176z	13	9	paths	path	NOUN
v979v12176z	13	10	represent	represent	VERB
v979v12176z	13	11	algebraically	algebraically	ADV
v979v12176z	13	12	independent	independent	ADJ
v979v12176z	13	13	reals	real	NOUN
v979v12176z	13	14	.	.	PUNCT
v979v12176z	14	1	we	we	PRON
v979v12176z	14	2	pass	pass	VERB
v979v12176z	14	3	from	from	ADP
v979v12176z	14	4	an	an	DET
v979v12176z	14	5	element	element	NOUN
v979v12176z	14	6	of	of	ADP
v979v12176z	14	7	dg	dg	PROPN
v979v12176z	14	8	to	to	ADP
v979v12176z	14	9	a	a	DET
v979v12176z	14	10	family	family	NOUN
v979v12176z	14	11	of	of	ADP
v979v12176z	14	12	paths	path	NOUN
v979v12176z	14	13	through	through	ADP
v979v12176z	14	14	t	t	PROPN
v979v12176z	14	15	,	,	PUNCT
v979v12176z	14	16	and	and	CCONJ
v979v12176z	14	17	from	from	ADP
v979v12176z	14	18	there	there	ADV
v979v12176z	14	19	to	to	ADP
v979v12176z	14	20	a	a	DET
v979v12176z	14	21	real	real	ADV
v979v12176z	14	22	closed	closed	ADJ
v979v12176z	14	23	field	field	NOUN
v979v12176z	14	24	which	which	PRON
v979v12176z	14	25	is	be	AUX
v979v12176z	14	26	the	the	DET
v979v12176z	14	27	real	real	ADJ
v979v12176z	14	28	closure	closure	NOUN
v979v12176z	14	29	of	of	ADP
v979v12176z	14	30	this	this	DET
v979v12176z	14	31	family	family	NOUN
v979v12176z	14	32	of	of	ADP
v979v12176z	14	33	reals.we	reals.we	X
v979v12176z	14	34	generalize	generalize	NOUN
v979v12176z	14	35	theorem	theorem	NOUN
v979v12176z	14	36	1	1	NUM
v979v12176z	14	37	and	and	CCONJ
v979v12176z	14	38	obtain	obtain	VERB
v979v12176z	14	39	the	the	DET
v979v12176z	14	40	following.theorem	following.theorem	ADJ
v979v12176z	14	41	2	2	NUM
v979v12176z	14	42	:	:	PUNCT
v979v12176z	14	43	let	let	VERB
v979v12176z	14	44	k	k	PROPN
v979v12176z	14	45	be	be	AUX
v979v12176z	14	46	a	a	DET
v979v12176z	14	47	class	class	NOUN
v979v12176z	14	48	of	of	ADP
v979v12176z	14	49	structures	structure	NOUN
v979v12176z	14	50	such	such	ADJ
v979v12176z	14	51	that	that	SCONJ
v979v12176z	14	52	any	any	DET
v979v12176z	14	53	a	a	DET
v979v12176z	14	54	,	,	PUNCT
v979v12176z	14	55	b	b	NOUN
v979v12176z	14	56	satisfying	satisfy	VERB
v979v12176z	14	57	the	the	DET
v979v12176z	14	58	same	same	ADJ
v979v12176z	14	59	quantifier	quantifier	NOUN
v979v12176z	14	60	-	-	PUNCT
v979v12176z	14	61	free	free	ADJ
v979v12176z	14	62	types	type	NOUN
v979v12176z	14	63	are	be	AUX
v979v12176z	14	64	isomorphic	isomorphic	ADJ
v979v12176z	14	65	.	.	PUNCT
v979v12176z	15	1	then	then	ADV
v979v12176z	15	2	k	k	PROPN
v979v12176z	15	3	<	<	X
v979v12176z	15	4	arcf.a	arcf.a	PROPN
v979v12176z	15	5	computable	computable	NOUN
v979v12176z	15	6	structure	structure	NOUN
v979v12176z	15	7	a	a	PRON
v979v12176z	15	8	is	be	AUX
v979v12176z	15	9	relatively	relatively	ADV
v979v12176z	15	10	delta	delta	ADJ
v979v12176z	15	11	-	-	PUNCT
v979v12176z	15	12	alpha	alpha	NOUN
v979v12176z	15	13	categorical	categorical	ADJ
v979v12176z	15	14	if	if	SCONJ
v979v12176z	15	15	for	for	ADP
v979v12176z	15	16	any	any	DET
v979v12176z	15	17	copy	copy	NOUN
v979v12176z	15	18	b	b	PROPN
v979v12176z	15	19	,	,	PUNCT
v979v12176z	15	20	isomorphicto	isomorphicto	PROPN
v979v12176z	15	21	a	a	PRON
v979v12176z	15	22	there	there	PRON
v979v12176z	15	23	is	be	VERB
v979v12176z	15	24	a	a	DET
v979v12176z	15	25	delta	delta	NOUN
v979v12176z	15	26	-	-	PUNCT
v979v12176z	15	27	alpha	alpha	NOUN
v979v12176z	15	28	relative	relative	ADJ
v979v12176z	15	29	to	to	ADP
v979v12176z	15	30	b	b	PROPN
v979v12176z	15	31	isomorphism	isomorphism	NOUN
v979v12176z	15	32	between	between	ADP
v979v12176z	15	33	a	a	PRON
v979v12176z	15	34	and	and	CCONJ
v979v12176z	15	35	b	b	NOUN
v979v12176z	15	36	,	,	PUNCT
v979v12176z	15	37	here	here	ADV
v979v12176z	15	38	'	'	PUNCT
v979v12176z	15	39	alpha	alpha	NOUN
v979v12176z	15	40	'	'	PUNCT
v979v12176z	15	41	stands	stand	VERB
v979v12176z	15	42	for	for	ADP
v979v12176z	15	43	a	a	DET
v979v12176z	15	44	computable	computable	ADJ
v979v12176z	15	45	ordinal	ordinal	NOUN
v979v12176z	15	46	.	.	PUNCT
v979v12176z	16	1	ash	ash	PROPN
v979v12176z	16	2	,	,	PUNCT
v979v12176z	16	3	knight	knight	NOUN
v979v12176z	16	4	,	,	PUNCT
v979v12176z	16	5	manasse	manasse	ADJ
v979v12176z	16	6	,	,	PUNCT
v979v12176z	16	7	and	and	CCONJ
v979v12176z	16	8	slaman	slaman	NOUN
v979v12176z	16	9	,	,	PUNCT
v979v12176z	16	10	and	and	CCONJ
v979v12176z	16	11	independently	independently	ADV
v979v12176z	16	12	chisholm	chisholm	ADJ
v979v12176z	16	13	,	,	PUNCT
v979v12176z	16	14	showed	show	VERB
v979v12176z	16	15	that	that	SCONJ
v979v12176z	16	16	a	a	DET
v979v12176z	16	17	structure	structure	NOUN
v979v12176z	16	18	is	be	AUX
v979v12176z	16	19	relatively	relatively	ADV
v979v12176z	16	20	delta	delta	ADJ
v979v12176z	16	21	-	-	PUNCT
v979v12176z	16	22	alpha	alpha	NOUN
v979v12176z	16	23	categorical	categorical	ADJ
v979v12176z	16	24	if	if	SCONJ
v979v12176z	16	25	it	it	PRON
v979v12176z	16	26	has	have	VERB
v979v12176z	16	27	a	a	DET
v979v12176z	16	28	formally	formally	ADV
v979v12176z	16	29	sigma	sigma	PROPN
v979v12176z	16	30	-	-	PUNCT
v979v12176z	16	31	alpha	alpha	NOUN
v979v12176z	16	32	scott	scott	PROPN
v979v12176z	16	33	family	family	NOUN
v979v12176z	16	34	of	of	ADP
v979v12176z	16	35	formulas	formula	NOUN
v979v12176z	16	36	.	.	PUNCT
v979v12176z	17	1	results	result	NOUN
v979v12176z	17	2	by	by	ADP
v979v12176z	17	3	nurtazin	nurtazin	PROPN
v979v12176z	17	4	imply	imply	VERB
v979v12176z	17	5	that	that	SCONJ
v979v12176z	17	6	a	a	DET
v979v12176z	17	7	real	real	ADJ
v979v12176z	17	8	closed	closed	ADJ
v979v12176z	17	9	field	field	NOUN
v979v12176z	17	10	is	be	AUX
v979v12176z	17	11	relatively	relatively	ADV
v979v12176z	17	12	computably	computably	ADV
v979v12176z	17	13	categorical	categorical	ADJ
v979v12176z	17	14	if	if	SCONJ
v979v12176z	17	15	it	it	PRON
v979v12176z	17	16	has	have	VERB
v979v12176z	17	17	finite	finite	ADJ
v979v12176z	17	18	transcendence	transcendence	NOUN
v979v12176z	17	19	degree	degree	NOUN
v979v12176z	17	20	.	.	PUNCT
v979v12176z	18	1	later	later	ADV
v979v12176z	18	2	work	work	NOUN
v979v12176z	18	3	by	by	ADP
v979v12176z	18	4	calvert	calvert	NOUN
v979v12176z	18	5	shows	show	VERB
v979v12176z	18	6	that	that	SCONJ
v979v12176z	18	7	if	if	SCONJ
v979v12176z	18	8	a	a	DET
v979v12176z	18	9	real	real	ADV
v979v12176z	18	10	closed	closed	ADJ
v979v12176z	18	11	field	field	NOUN
v979v12176z	18	12	is	be	AUX
v979v12176z	18	13	archimedean	archimedean	ADJ
v979v12176z	18	14	then	then	ADV
v979v12176z	18	15	it	it	PRON
v979v12176z	18	16	is	be	AUX
v979v12176z	18	17	relatively	relatively	ADV
v979v12176z	18	18	delta-2	delta-2	ADJ
v979v12176z	18	19	categorical.marker	categorical.marker	NOUN
v979v12176z	18	20	's	's	PART
v979v12176z	18	21	embedding	embedding	NOUN
v979v12176z	18	22	takes	take	VERB
v979v12176z	18	23	a	a	DET
v979v12176z	18	24	linear	linear	ADJ
v979v12176z	18	25	order	order	NOUN
v979v12176z	18	26	l	l	NOUN
v979v12176z	18	27	to	to	ADP
v979v12176z	18	28	a	a	DET
v979v12176z	18	29	real	real	ADV
v979v12176z	18	30	closed	closed	ADJ
v979v12176z	18	31	field	field	NOUN
v979v12176z	18	32	we	we	PRON
v979v12176z	18	33	denote	denote	VERB
v979v12176z	18	34	by	by	ADP
v979v12176z	18	35	rl	rl	PROPN
v979v12176z	18	36	.	.	PUNCT
v979v12176z	19	1	essentially	essentially	ADV
v979v12176z	19	2	rl	rl	PROPN
v979v12176z	19	3	is	be	AUX
v979v12176z	19	4	the	the	DET
v979v12176z	19	5	real	real	ADJ
v979v12176z	19	6	closure	closure	NOUN
v979v12176z	19	7	of	of	ADP
v979v12176z	19	8	l	l	PROPN
v979v12176z	19	9	,	,	PUNCT
v979v12176z	19	10	where	where	SCONJ
v979v12176z	19	11	the	the	DET
v979v12176z	19	12	elements	element	NOUN
v979v12176z	19	13	of	of	ADP
v979v12176z	19	14	l	l	PRON
v979v12176z	19	15	are	be	AUX
v979v12176z	19	16	positive	positive	ADJ
v979v12176z	19	17	and	and	CCONJ
v979v12176z	19	18	infinite	infinite	ADJ
v979v12176z	19	19	in	in	ADP
v979v12176z	19	20	rl	rl	PROPN
v979v12176z	19	21	,	,	PUNCT
v979v12176z	19	22	and	and	CCONJ
v979v12176z	19	23	if	if	SCONJ
v979v12176z	19	24	l	l	PRON
v979v12176z	19	25	is	be	AUX
v979v12176z	19	26	less	less	ADJ
v979v12176z	19	27	than	than	SCONJ
v979v12176z	19	28	s	s	VERB
v979v12176z	19	29	in	in	ADP
v979v12176z	19	30	l	l	PROPN
v979v12176z	19	31	,	,	PUNCT
v979v12176z	19	32	then	then	ADV
v979v12176z	19	33	all	all	DET
v979v12176z	19	34	positive	positive	ADJ
v979v12176z	19	35	powers	power	NOUN
v979v12176z	19	36	of	of	ADP
v979v12176z	19	37	l	l	PRON
v979v12176z	19	38	are	be	AUX
v979v12176z	19	39	less	less	ADJ
v979v12176z	19	40	than	than	SCONJ
v979v12176z	19	41	s	s	VERB
v979v12176z	19	42	in	in	ADP
v979v12176z	19	43	rl.theorem	rl.theorem	VERB
v979v12176z	19	44	3	3	NUM
v979v12176z	19	45	:	:	PUNCT
v979v12176z	19	46	if	if	SCONJ
v979v12176z	19	47	a	a	DET
v979v12176z	19	48	computable	computable	ADJ
v979v12176z	19	49	linear	linear	NOUN
v979v12176z	19	50	order	order	NOUN
v979v12176z	19	51	l	l	PRON
v979v12176z	19	52	is	be	AUX
v979v12176z	19	53	relatively	relatively	ADV
v979v12176z	19	54	delta	delta	ADJ
v979v12176z	19	55	-	-	PUNCT
v979v12176z	19	56	alpha	alpha	NOUN
v979v12176z	19	57	categorical	categorical	ADJ
v979v12176z	19	58	,	,	PUNCT
v979v12176z	19	59	then	then	ADV
v979v12176z	19	60	rl	rl	PROPN
v979v12176z	19	61	isrelatively	isrelatively	ADV
v979v12176z	19	62	delta-(1+alpha	delta-(1+alpha	SPACE
v979v12176z	19	63	)	)	PUNCT
v979v12176z	19	64	categorical.the	categorical.the	DET
v979v12176z	19	65	converse	converse	NOUN
v979v12176z	19	66	of	of	ADP
v979v12176z	19	67	theorem	theorem	NOUN
v979v12176z	19	68	3	3	NUM
v979v12176z	19	69	holds	hold	VERB
v979v12176z	19	70	for	for	ADP
v979v12176z	19	71	alpha	alpha	NOUN
v979v12176z	19	72	=	=	NOUN
v979v12176z	19	73	1	1	NUM
v979v12176z	19	74	.	.	PUNCT
v979v12176z	20	1	we	we	PRON
v979v12176z	20	2	show	show	VERB
v979v12176z	20	3	it	it	PRON
v979v12176z	20	4	also	also	ADV
v979v12176z	20	5	holds	hold	VERB
v979v12176z	20	6	for	for	ADP
v979v12176z	20	7	alpha	alpha	NOUN
v979v12176z	20	8	a	a	DET
v979v12176z	20	9	natural	natural	ADJ
v979v12176z	20	10	number	number	NOUN
v979v12176z	20	11	,	,	PUNCT
v979v12176z	20	12	assuming	assume	VERB
v979v12176z	20	13	further	further	ADJ
v979v12176z	20	14	computability	computability	NOUN
v979v12176z	20	15	properties	property	NOUN
v979v12176z	20	16	on	on	ADP
v979v12176z	20	17	one	one	NUM
v979v12176z	20	18	copy	copy	NOUN
v979v12176z	20	19	of	of	ADP
v979v12176z	20	20	l.	l.	PROPN
v979v12176z	20	21	we	we	PRON
v979v12176z	20	22	are	be	AUX
v979v12176z	20	23	able	able	ADJ
v979v12176z	20	24	then	then	ADV
v979v12176z	20	25	to	to	PART
v979v12176z	20	26	show	show	VERB
v979v12176z	20	27	the	the	DET
v979v12176z	20	28	following.theorem	following.theorem	ADJ
v979v12176z	20	29	4	4	NUM
v979v12176z	20	30	:	:	PUNCT
v979v12176z	20	31	for	for	ADP
v979v12176z	20	32	arbitrarily	arbitrarily	ADV
v979v12176z	20	33	large	large	ADJ
v979v12176z	20	34	computable	computable	ADJ
v979v12176z	20	35	ordinals	ordinal	NOUN
v979v12176z	20	36	,	,	PUNCT
v979v12176z	20	37	there	there	PRON
v979v12176z	20	38	is	be	VERB
v979v12176z	20	39	a	a	DET
v979v12176z	20	40	real	real	ADV
v979v12176z	20	41	closed	closed	ADJ
v979v12176z	20	42	field	field	NOUN
v979v12176z	20	43	that	that	PRON
v979v12176z	20	44	is	be	AUX
v979v12176z	20	45	relatively	relatively	ADV
v979v12176z	20	46	delta	delta	ADJ
v979v12176z	20	47	-	-	PUNCT
v979v12176z	20	48	alpha	alpha	NOUN
v979v12176z	20	49	categorical	categorical	ADJ
v979v12176z	20	50	and	and	CCONJ
v979v12176z	20	51	not	not	PART
v979v12176z	20	52	relatively	relatively	ADV
v979v12176z	20	53	delta	delta	ADJ
v979v12176z	20	54	-	-	PUNCT
v979v12176z	20	55	beta	beta	NOUN
v979v12176z	20	56	categorical	categorical	NOUN
v979v12176z	20	57	for	for	ADP
v979v12176z	20	58	any	any	DET
v979v12176z	20	59	ordinal	ordinal	ADJ
v979v12176z	20	60	beta	beta	NOUN
v979v12176z	20	61	less	less	ADJ
v979v12176z	20	62	than	than	ADP
v979v12176z	20	63	alpha	alpha	NOUN
v979v12176z	20	64	.	.	PUNCT