Nearly Projective Boolean Algebras Book

	Introduction	1
	Overview	3
	Prerequisites and notation	8
1	Setting the stage	11
1.1	Clubs, skeletons and filtrations	11
1.2	Three types of embeddings	14
1.3	Projective Boolean algebras	22
1.4	Free extensions	25
1.5	Projective embeddings	31
2	rc-filtered Boolean algebras	37
2.1	rc-filtrations	37
2.2	The Freese/Nation property	40
2.3	Subalgebras	44
2.4	Homomorphic images	47
2.5	Products	51
2.6	First results about cardinal functions	53
2.7	Computation of cardinal functions	56
2.8	The free algebra on N[subscript 1] generators	60
2.9	[kappa]-metrization	64
2.10	Answers to some questions of Scepin	66
3	Functors	69
3.1	Generalities	69
3.2	Superextensions	72
3.3	Exponentials	78
3.4	Symmetric powers	90
4	[sigma]-filtered Boolean algebras	97
4.1	Commuting subalgebras	97
4.2	The weak Freese/Nation property	100
4.3	The strong Freese/Nation property	106
5	Weakly projective algebras	111
5.1	Completions and co-completeness	111
5.2	Cohen algebras	115
5.3	Characterizations of weak projectivity	123
5.4	Adequateness and closedness properties	134
5.5	Regularly filtered algebras	140
6	The twisted embedding	147
6.1	The basic square	147
6.2	Twisted embeddings	151
6.3	The non-weakly projective example	159
6.4	On the number of rc-filtered Boolean algebras	160
	A. Set-theoretic aspects	165
A.1	Elementary substructures of [actual symbol not reproducible]	165
A.2	Characterizations	176
A.3	Answers to some other questions of Scepin	183
A.4	N[subscript 2]-projectively filtered Boolean algebras	186
A.5	Forcing projectivity	192
	References	195
	Index	200