id	sid	tid	token	lemma	pos
7m01bk15c0w	1	1	given	give	VERB
7m01bk15c0w	1	2	a	a	DET
7m01bk15c0w	1	3	finite	finite	ADJ
7m01bk15c0w	1	4	lattice	lattice	NOUN
7m01bk15c0w	1	5	l	l	NOUN
7m01bk15c0w	1	6	that	that	PRON
7m01bk15c0w	1	7	can	can	AUX
7m01bk15c0w	1	8	be	be	AUX
7m01bk15c0w	1	9	embedded	embed	VERB
7m01bk15c0w	1	10	in	in	ADP
7m01bk15c0w	1	11	the	the	DET
7m01bk15c0w	1	12	recursively	recursively	ADV
7m01bk15c0w	1	13	enumerable	enumerable	ADJ
7m01bk15c0w	1	14	(	(	PUNCT
7m01bk15c0w	1	15	r.e	r.e	PROPN
7m01bk15c0w	1	16	.	.	PUNCT
7m01bk15c0w	1	17	)	)	PUNCT
7m01bk15c0w	1	18	turing	ture	VERB
7m01bk15c0w	1	19	degrees	degree	NOUN
7m01bk15c0w	1	20	(	(	PUNCT
7m01bk15c0w	1	21	rt	rt	PROPN
7m01bk15c0w	1	22	,	,	PUNCT
7m01bk15c0w	1	23	≤t	≤t	PROPN
7m01bk15c0w	1	24	)	)	PUNCT
7m01bk15c0w	1	25	,	,	PUNCT
7m01bk15c0w	1	26	we	we	PRON
7m01bk15c0w	1	27	do	do	AUX
7m01bk15c0w	1	28	not	not	PART
7m01bk15c0w	1	29	in	in	ADP
7m01bk15c0w	1	30	general	general	ADJ
7m01bk15c0w	1	31	know	know	VERB
7m01bk15c0w	1	32	how	how	SCONJ
7m01bk15c0w	1	33	to	to	PART
7m01bk15c0w	1	34	characterize	characterize	VERB
7m01bk15c0w	1	35	the	the	DET
7m01bk15c0w	1	36	degrees	degree	NOUN
7m01bk15c0w	1	37	d	d	X
7m01bk15c0w	1	38	ε	ε	X
7m01bk15c0w	1	39	rt	rt	PROPN
7m01bk15c0w	1	40	below	below	ADP
7m01bk15c0w	1	41	which	which	PRON
7m01bk15c0w	1	42	l	l	PRON
7m01bk15c0w	1	43	can	can	AUX
7m01bk15c0w	1	44	be	be	AUX
7m01bk15c0w	1	45	bounded	bound	VERB
7m01bk15c0w	1	46	.	.	PUNCT
7m01bk15c0w	2	1	the	the	DET
7m01bk15c0w	2	2	important	important	ADJ
7m01bk15c0w	2	3	characterizations	characterization	NOUN
7m01bk15c0w	2	4	known	know	VERB
7m01bk15c0w	2	5	are	be	AUX
7m01bk15c0w	2	6	of	of	ADP
7m01bk15c0w	2	7	the	the	DET
7m01bk15c0w	2	8	l7	l7	PROPN
7m01bk15c0w	2	9	and	and	CCONJ
7m01bk15c0w	2	10	m3	m3	PROPN
7m01bk15c0w	2	11	lattices	lattice	NOUN
7m01bk15c0w	2	12	,	,	PUNCT
7m01bk15c0w	2	13	where	where	SCONJ
7m01bk15c0w	2	14	the	the	DET
7m01bk15c0w	2	15	lattices	lattice	NOUN
7m01bk15c0w	2	16	are	be	AUX
7m01bk15c0w	2	17	bounded	bound	VERB
7m01bk15c0w	2	18	below	below	ADP
7m01bk15c0w	2	19	d	d	NOUN
7m01bk15c0w	2	20	if	if	SCONJ
7m01bk15c0w	2	21	and	and	CCONJ
7m01bk15c0w	2	22	only	only	ADV
7m01bk15c0w	2	23	if	if	SCONJ
7m01bk15c0w	2	24	d	d	NOUN
7m01bk15c0w	2	25	contains	contain	VERB
7m01bk15c0w	2	26	sets	set	NOUN
7m01bk15c0w	2	27	of	of	ADP
7m01bk15c0w	2	28	"	"	PUNCT
7m01bk15c0w	2	29	fickleness	fickleness	NOUN
7m01bk15c0w	2	30	"	"	PUNCT
7m01bk15c0w	2	31	&	&	CCONJ
7m01bk15c0w	2	32	gt;ω	gt;ω	PROPN
7m01bk15c0w	2	33	and	and	CCONJ
7m01bk15c0w	2	34	≥ωω	≥ωω	NUM
7m01bk15c0w	2	35	respectively	respectively	ADV
7m01bk15c0w	2	36	.	.	PUNCT
7m01bk15c0w	3	1	we	we	PRON
7m01bk15c0w	3	2	work	work	VERB
7m01bk15c0w	3	3	towards	towards	ADP
7m01bk15c0w	3	4	finding	find	VERB
7m01bk15c0w	3	5	a	a	DET
7m01bk15c0w	3	6	lattice	lattice	NOUN
7m01bk15c0w	3	7	that	that	PRON
7m01bk15c0w	3	8	characterizes	characterize	VERB
7m01bk15c0w	3	9	the	the	DET
7m01bk15c0w	3	10	levels	level	NOUN
7m01bk15c0w	3	11	above	above	ADP
7m01bk15c0w	3	12	ω2	ω2	PROPN
7m01bk15c0w	3	13	,	,	PUNCT
7m01bk15c0w	3	14	the	the	DET
7m01bk15c0w	3	15	first	first	ADJ
7m01bk15c0w	3	16	non	non	ADJ
7m01bk15c0w	3	17	-	-	ADJ
7m01bk15c0w	3	18	trivial	trivial	ADJ
7m01bk15c0w	3	19	level	level	NOUN
7m01bk15c0w	3	20	after	after	ADP
7m01bk15c0w	3	21	ω	ω	PROPN
7m01bk15c0w	3	22	.	.	PUNCT
7m01bk15c0w	4	1	we	we	PRON
7m01bk15c0w	4	2	introduced	introduce	VERB
7m01bk15c0w	4	3	a	a	DET
7m01bk15c0w	4	4	lattice	lattice	ADJ
7m01bk15c0w	4	5	-	-	PUNCT
7m01bk15c0w	4	6	theoretic	theoretic	ADJ
7m01bk15c0w	4	7	property	property	NOUN
7m01bk15c0w	4	8	called	call	VERB
7m01bk15c0w	4	9	"	"	PUNCT
7m01bk15c0w	4	10	3	3	NUM
7m01bk15c0w	4	11	-	-	PUNCT
7m01bk15c0w	4	12	directness	directness	ADJ
7m01bk15c0w	4	13	"	"	PUNCT
7m01bk15c0w	4	14	to	to	PART
7m01bk15c0w	4	15	describe	describe	VERB
7m01bk15c0w	4	16	lattices	lattice	NOUN
7m01bk15c0w	4	17	that	that	PRON
7m01bk15c0w	4	18	are	be	AUX
7m01bk15c0w	4	19	no	no	DET
7m01bk15c0w	4	20	"	"	PUNCT
7m01bk15c0w	4	21	wider	wide	ADJ
7m01bk15c0w	4	22	"	"	PUNCT
7m01bk15c0w	4	23	or	or	CCONJ
7m01bk15c0w	4	24	"	"	PUNCT
7m01bk15c0w	4	25	taller	tall	ADJ
7m01bk15c0w	4	26	"	"	PUNCT
7m01bk15c0w	4	27	than	than	ADP
7m01bk15c0w	4	28	l7	l7	PROPN
7m01bk15c0w	4	29	and	and	CCONJ
7m01bk15c0w	4	30	m3	m3	PROPN
7m01bk15c0w	4	31	.	.	PUNCT
7m01bk15c0w	5	1	we	we	PRON
7m01bk15c0w	5	2	exhaust	exhaust	VERB
7m01bk15c0w	5	3	the	the	DET
7m01bk15c0w	5	4	3	3	NUM
7m01bk15c0w	5	5	-	-	PUNCT
7m01bk15c0w	5	6	direct	direct	ADJ
7m01bk15c0w	5	7	lattices	lattice	NOUN
7m01bk15c0w	5	8	l	l	NOUN
7m01bk15c0w	5	9	,	,	PUNCT
7m01bk15c0w	5	10	but	but	CCONJ
7m01bk15c0w	5	11	they	they	PRON
7m01bk15c0w	5	12	turn	turn	VERB
7m01bk15c0w	5	13	out	out	ADP
7m01bk15c0w	5	14	to	to	PART
7m01bk15c0w	5	15	also	also	ADV
7m01bk15c0w	5	16	characterize	characterize	VERB
7m01bk15c0w	5	17	the	the	PRON
7m01bk15c0w	5	18	&	&	CCONJ
7m01bk15c0w	5	19	gt;ω	gt;ω	PROPN
7m01bk15c0w	5	20	or	or	CCONJ
7m01bk15c0w	5	21	≥ωω	≥ωω	NUM
7m01bk15c0w	5	22	levels	level	NOUN
7m01bk15c0w	5	23	,	,	PUNCT
7m01bk15c0w	5	24	if	if	SCONJ
7m01bk15c0w	5	25	l	l	PRON
7m01bk15c0w	5	26	is	be	AUX
7m01bk15c0w	5	27	not	not	PART
7m01bk15c0w	5	28	already	already	ADV
7m01bk15c0w	5	29	embeddable	embeddable	ADJ
7m01bk15c0w	5	30	below	below	ADP
7m01bk15c0w	5	31	all	all	DET
7m01bk15c0w	5	32	non	non	ADJ
7m01bk15c0w	5	33	-	-	ADJ
7m01bk15c0w	5	34	zero	zero	ADJ
7m01bk15c0w	5	35	r.e	r.e	NOUN
7m01bk15c0w	5	36	.	.	PUNCT
7m01bk15c0w	5	37	degrees	degree	NOUN
7m01bk15c0w	5	38	.	.	PUNCT
7m01bk15c0w	6	1	we	we	PRON
7m01bk15c0w	6	2	also	also	ADV
7m01bk15c0w	6	3	considered	consider	VERB
7m01bk15c0w	6	4	upper	upper	ADJ
7m01bk15c0w	6	5	semilattices	semilattice	NOUN
7m01bk15c0w	6	6	(	(	PUNCT
7m01bk15c0w	6	7	usls	usls	NOUN
7m01bk15c0w	6	8	)	)	PUNCT
7m01bk15c0w	6	9	by	by	ADP
7m01bk15c0w	6	10	removing	remove	VERB
7m01bk15c0w	6	11	the	the	DET
7m01bk15c0w	6	12	bottom	bottom	ADJ
7m01bk15c0w	6	13	meet(s	meet(s	PROPN
7m01bk15c0w	6	14	)	)	PUNCT
7m01bk15c0w	6	15	of	of	ADP
7m01bk15c0w	6	16	some	some	DET
7m01bk15c0w	6	17	3	3	NUM
7m01bk15c0w	6	18	-	-	PUNCT
7m01bk15c0w	6	19	direct	direct	ADJ
7m01bk15c0w	6	20	lattices	lattice	NOUN
7m01bk15c0w	6	21	,	,	PUNCT
7m01bk15c0w	6	22	but	but	CCONJ
7m01bk15c0w	6	23	the	the	DET
7m01bk15c0w	6	24	removals	removal	NOUN
7m01bk15c0w	6	25	did	do	AUX
7m01bk15c0w	6	26	not	not	PART
7m01bk15c0w	6	27	change	change	VERB
7m01bk15c0w	6	28	the	the	DET
7m01bk15c0w	6	29	levels	level	NOUN
7m01bk15c0w	6	30	characterized	characterize	VERB
7m01bk15c0w	6	31	.	.	PUNCT
7m01bk15c0w	7	1	this	this	PRON
7m01bk15c0w	7	2	leads	lead	VERB
7m01bk15c0w	7	3	us	we	PRON
7m01bk15c0w	7	4	to	to	PART
7m01bk15c0w	7	5	conjecture	conjecture	VERB
7m01bk15c0w	7	6	that	that	SCONJ
7m01bk15c0w	7	7	a	a	DET
7m01bk15c0w	7	8	usl	usl	PROPN
7m01bk15c0w	7	9	characterizes	characterize	VERB
7m01bk15c0w	7	10	the	the	DET
7m01bk15c0w	7	11	same	same	ADJ
7m01bk15c0w	7	12	r.e	r.e	NOUN
7m01bk15c0w	7	13	.	.	PUNCT
7m01bk15c0w	7	14	degrees	degree	NOUN
7m01bk15c0w	7	15	as	as	ADP
7m01bk15c0w	7	16	the	the	DET
7m01bk15c0w	7	17	lattice	lattice	NOUN
7m01bk15c0w	7	18	on	on	ADP
7m01bk15c0w	7	19	which	which	PRON
7m01bk15c0w	7	20	the	the	DET
7m01bk15c0w	7	21	usl	usl	PROPN
7m01bk15c0w	7	22	is	be	AUX
7m01bk15c0w	7	23	based	base	VERB
7m01bk15c0w	7	24	.	.	PUNCT
7m01bk15c0w	8	1	we	we	PRON
7m01bk15c0w	8	2	discovered	discover	VERB
7m01bk15c0w	8	3	three	three	NUM
7m01bk15c0w	8	4	3	3	NUM
7m01bk15c0w	8	5	-	-	PUNCT
7m01bk15c0w	8	6	direct	direct	ADJ
7m01bk15c0w	8	7	lattices	lattice	NOUN
7m01bk15c0w	8	8	besides	besides	SCONJ
7m01bk15c0w	8	9	m3	m3	PROPN
7m01bk15c0w	8	10	that	that	PRON
7m01bk15c0w	8	11	also	also	ADV
7m01bk15c0w	8	12	characterize	characterize	VERB
7m01bk15c0w	8	13	the	the	DET
7m01bk15c0w	8	14	≥ωω	≥ωω	NUM
7m01bk15c0w	8	15	-levels	-level	NOUN
7m01bk15c0w	8	16	.	.	PUNCT
7m01bk15c0w	9	1	our	our	PRON
7m01bk15c0w	9	2	search	search	NOUN
7m01bk15c0w	9	3	for	for	ADP
7m01bk15c0w	9	4	a	a	DET
7m01bk15c0w	9	5	&	&	CCONJ
7m01bk15c0w	9	6	gt;ω2	gt;ω2	NOUN
7m01bk15c0w	9	7	-	-	PUNCT
7m01bk15c0w	9	8	candidate	candidate	NOUN
7m01bk15c0w	9	9	therefore	therefore	ADV
7m01bk15c0w	9	10	involves	involve	VERB
7m01bk15c0w	9	11	the	the	DET
7m01bk15c0w	9	12	lattice	lattice	ADJ
7m01bk15c0w	9	13	-	-	PUNCT
7m01bk15c0w	9	14	theoretic	theoretic	ADJ
7m01bk15c0w	9	15	problem	problem	NOUN
7m01bk15c0w	9	16	of	of	ADP
7m01bk15c0w	9	17	finding	find	VERB
7m01bk15c0w	9	18	lattices	lattice	NOUN
7m01bk15c0w	9	19	that	that	PRON
7m01bk15c0w	9	20	do	do	AUX
7m01bk15c0w	9	21	not	not	PART
7m01bk15c0w	9	22	contain	contain	VERB
7m01bk15c0w	9	23	any	any	PRON
7m01bk15c0w	9	24	of	of	ADP
7m01bk15c0w	9	25	the	the	DET
7m01bk15c0w	9	26	four	four	NUM
7m01bk15c0w	9	27	≥ωω	≥ωω	SPACE
7m01bk15c0w	9	28	-	-	PUNCT
7m01bk15c0w	9	29	lattices	lattice	NOUN
7m01bk15c0w	9	30	as	as	ADP
7m01bk15c0w	9	31	sublattices	sublattice	NOUN
7m01bk15c0w	9	32	.	.	PUNCT