id	sid	tid	token	lemma	pos
3r074t66b55	1	1	the	the	DET
3r074t66b55	1	2	pi-0	pi-0	SPACE
3r074t66b55	1	3	-	-	PUNCT
3r074t66b55	1	4	1	1	NUM
3r074t66b55	1	5	classes	class	NOUN
3r074t66b55	1	6	have	have	AUX
3r074t66b55	1	7	become	become	VERB
3r074t66b55	1	8	important	important	ADJ
3r074t66b55	1	9	structures	structure	NOUN
3r074t66b55	1	10	in	in	ADP
3r074t66b55	1	11	computability	computability	NOUN
3r074t66b55	1	12	theory	theory	NOUN
3r074t66b55	1	13	.	.	PUNCT
3r074t66b55	2	1	related	relate	VERB
3r074t66b55	2	2	to	to	ADP
3r074t66b55	2	3	the	the	DET
3r074t66b55	2	4	study	study	NOUN
3r074t66b55	2	5	of	of	ADP
3r074t66b55	2	6	properties	property	NOUN
3r074t66b55	2	7	of	of	ADP
3r074t66b55	2	8	individual	individual	ADJ
3r074t66b55	2	9	classes	class	NOUN
3r074t66b55	2	10	is	be	AUX
3r074t66b55	2	11	the	the	DET
3r074t66b55	2	12	study	study	NOUN
3r074t66b55	2	13	of	of	ADP
3r074t66b55	2	14	the	the	DET
3r074t66b55	2	15	lattice	lattice	NOUN
3r074t66b55	2	16	of	of	ADP
3r074t66b55	2	17	all	all	DET
3r074t66b55	2	18	pi-0	pi-0	PROPN
3r074t66b55	2	19	-	-	PUNCT
3r074t66b55	2	20	1	1	NUM
3r074t66b55	2	21	classes	class	NOUN
3r074t66b55	2	22	,	,	PUNCT
3r074t66b55	2	23	denoted	denote	VERB
3r074t66b55	2	24	e_pi	e_pi	NOUN
3r074t66b55	2	25	.	.	PUNCT
3r074t66b55	3	1	we	we	PRON
3r074t66b55	3	2	define	define	VERB
3r074t66b55	3	3	a	a	DET
3r074t66b55	3	4	substructure	substructure	NOUN
3r074t66b55	3	5	of	of	ADP
3r074t66b55	3	6	e_pi	e_pi	PROPN
3r074t66b55	3	7	,	,	PUNCT
3r074t66b55	3	8	g	g	NOUN
3r074t66b55	3	9	=	=	X
3r074t66b55	4	1	[	[	X
3r074t66b55	4	2	n	n	X
3r074t66b55	4	3	,	,	PUNCT
3r074t66b55	4	4	2^omega	2^omega	NUM
3r074t66b55	4	5	]	]	PUNCT
3r074t66b55	4	6	for	for	ADP
3r074t66b55	4	7	n	n	NOUN
3r074t66b55	4	8	nonprincipal	nonprincipal	NOUN
3r074t66b55	4	9	,	,	PUNCT
3r074t66b55	4	10	and	and	CCONJ
3r074t66b55	4	11	a	a	DET
3r074t66b55	4	12	quotient	quotient	NOUN
3r074t66b55	4	13	structure	structure	NOUN
3r074t66b55	4	14	of	of	ADP
3r074t66b55	4	15	g	g	PROPN
3r074t66b55	4	16	,	,	PUNCT
3r074t66b55	4	17	denoted	denote	VERB
3r074t66b55	4	18	g^diamond	g^diamond	PROPN
3r074t66b55	4	19	and	and	CCONJ
3r074t66b55	4	20	thought	think	VERB
3r074t66b55	4	21	of	of	ADP
3r074t66b55	4	22	as	as	SCONJ
3r074t66b55	4	23	g	g	PROPN
3r074t66b55	4	24	modulo	modulo	NOUN
3r074t66b55	4	25	principal	principal	ADJ
3r074t66b55	4	26	classes	class	NOUN
3r074t66b55	4	27	disjoint	disjoint	ADV
3r074t66b55	4	28	from	from	ADP
3r074t66b55	4	29	n.	n.	PROPN
3r074t66b55	4	30	using	use	VERB
3r074t66b55	4	31	the	the	DET
3r074t66b55	4	32	setting	setting	NOUN
3r074t66b55	4	33	of	of	ADP
3r074t66b55	4	34	computably	computably	ADV
3r074t66b55	4	35	enumerable	enumerable	ADJ
3r074t66b55	4	36	ideals	ideal	NOUN
3r074t66b55	4	37	,	,	PUNCT
3r074t66b55	4	38	we	we	PRON
3r074t66b55	4	39	present	present	VERB
3r074t66b55	4	40	basic	basic	ADJ
3r074t66b55	4	41	results	result	NOUN
3r074t66b55	4	42	for	for	ADP
3r074t66b55	4	43	g	g	PROPN
3r074t66b55	4	44	and	and	CCONJ
3r074t66b55	4	45	g^diamond	g^diamond	PROPN
3r074t66b55	4	46	and	and	CCONJ
3r074t66b55	4	47	show	show	VERB
3r074t66b55	4	48	that	that	SCONJ
3r074t66b55	4	49	g^diamond	g^diamond	PROPN
3r074t66b55	4	50	is	be	AUX
3r074t66b55	4	51	isomorphic	isomorphic	ADJ
3r074t66b55	4	52	to	to	PART
3r074t66b55	4	53	e	e	VERB
3r074t66b55	4	54	*	*	PROPN
3r074t66b55	4	55	,	,	PUNCT
3r074t66b55	4	56	the	the	DET
3r074t66b55	4	57	lattice	lattice	NOUN
3r074t66b55	4	58	of	of	ADP
3r074t66b55	4	59	computably	computably	ADV
3r074t66b55	4	60	enumerable	enumerable	ADJ
3r074t66b55	4	61	sets	set	NOUN
3r074t66b55	4	62	modulo	modulo	NOUN
3r074t66b55	4	63	finite	finite	NOUN
3r074t66b55	4	64	difference	difference	NOUN
3r074t66b55	4	65	.	.	PUNCT
3r074t66b55	5	1	this	this	DET
3r074t66b55	5	2	isomorphism	isomorphism	NOUN
3r074t66b55	5	3	allows	allow	VERB
3r074t66b55	5	4	us	we	PRON
3r074t66b55	5	5	to	to	PART
3r074t66b55	5	6	transfer	transfer	VERB
3r074t66b55	5	7	invariant	invariant	ADJ
3r074t66b55	5	8	classes	class	NOUN
3r074t66b55	5	9	from	from	ADP
3r074t66b55	5	10	e	e	NOUN
3r074t66b55	5	11	*	*	PUNCT
3r074t66b55	5	12	to	to	ADP
3r074t66b55	5	13	e_pi	e_pi	PROPN
3r074t66b55	5	14	.	.	PUNCT
3r074t66b55	6	1	however	however	ADV
3r074t66b55	6	2	,	,	PUNCT
3r074t66b55	6	3	it	it	PRON
3r074t66b55	6	4	does	do	AUX
3r074t66b55	6	5	not	not	PART
3r074t66b55	6	6	in	in	ADP
3r074t66b55	6	7	general	general	ADJ
3r074t66b55	6	8	allow	allow	VERB
3r074t66b55	6	9	the	the	DET
3r074t66b55	6	10	transfer	transfer	NOUN
3r074t66b55	6	11	of	of	ADP
3r074t66b55	6	12	orbits	orbit	NOUN
3r074t66b55	6	13	.	.	PUNCT
3r074t66b55	7	1	we	we	PRON
3r074t66b55	7	2	give	give	VERB
3r074t66b55	7	3	the	the	DET
3r074t66b55	7	4	conditions	condition	NOUN
3r074t66b55	7	5	under	under	ADP
3r074t66b55	7	6	which	which	PRON
3r074t66b55	7	7	an	an	DET
3r074t66b55	7	8	orbit	orbit	NOUN
3r074t66b55	7	9	could	could	AUX
3r074t66b55	7	10	transfer	transfer	VERB
3r074t66b55	7	11	and	and	CCONJ
3r074t66b55	7	12	an	an	DET
3r074t66b55	7	13	example	example	NOUN
3r074t66b55	7	14	of	of	ADP
3r074t66b55	7	15	one	one	NOUN
3r074t66b55	7	16	which	which	PRON
3r074t66b55	7	17	does	do	VERB
3r074t66b55	7	18	,	,	PUNCT
3r074t66b55	7	19	and	and	CCONJ
3r074t66b55	7	20	conclude	conclude	VERB
3r074t66b55	7	21	with	with	ADP
3r074t66b55	7	22	open	open	ADJ
3r074t66b55	7	23	questions	question	NOUN
3r074t66b55	7	24	related	relate	VERB
3r074t66b55	7	25	to	to	ADP
3r074t66b55	7	26	degree	degree	NOUN
3r074t66b55	7	27	-	-	PUNCT
3r074t66b55	7	28	theoretic	theoretic	ADJ
3r074t66b55	7	29	properties	property	NOUN
3r074t66b55	7	30	.	.	PUNCT