Ramsey Theory References
                  A. Miller Mar 92


Carlson, Some unifying principles in Ramsey Theory, Disc. Math. 68
(1988) 117-169.  Abstract Ellentuck theorem.

Carlson, Graham-Leeb-Rothschild Thm, J. Comb Thy 44 (1987) 22-33.
 Infinite version of vector space Ramsey theorem.

Carlson-Simpson, Dual Ramsey Theory, Adv. in Math. 53 (1984) 265-290.

Carlson-Simpson, Topological Ramsey Theory, in Mathematics of Ramsey
Theory, Algor. Comp. 5 , Springer 1990, 172-183.  Every set is
abstract Ramsey in Solovay's model.

Graham-Rothschild-Spencer, Ramsey Theory, Wiley 1980. Second edition
has Shelah's proof.

Laver,  Products of infinitely many perfect trees   J. London Math.
Soc. 29 (1984) 385-396.  Infinite product version of Halpern-Leuchli.

Promel-Voigt, Measurable Ramsey Theory, Combinatorica, 11 (1991) 253-251.

Shelah, van der Waerden Theorem, JAMS 1 (1988) 683-697.



                Solovay Model References
                  A. Miller Apr 92


Bartoszynski, Additivity of measure implies additivity of category,
Trans AMS, 281(1984) 209-213.

Bartoszynski-Judah, All meager filters may be null, Proc AMS,

Bekkali, Topics in Set Theory, Lecture Notes in Math 1476, Springer (1991).

Blass, Selective ultrafilters and homogeneity, Ann Pure Appl Logic
38(1988) 215-255. In the Levy collapse of a Mahlo cardinal any
selective ultrafilter is generic over the Solovay model.

Fremlin, On the additivity and cofinality of Radon measures,
Mathematika 31(1984) 323-335.

Fujita, Mansfield and Solovay type results on covering plane sets by
lines,  Nagoya Math J.   In Solovay's model every subset of the plane
which can't be covered by countably many lines contains a perfect set with
no three points collinear.

Grigorieff, Intermediate submodels and generic extensions of set
theory, Ann of Math, 101(1975) 447-490.  Every intermediate model
is itself set-generic over the ground model.

Harrington-Shelah, Some exact equiconsistency results in set theory,
Notre Dame J of Formal Logic, 26(1985) 178-184.  Exists a Mahlo is
equiconsistent with MA + notCH + Delta^1_3(LM).

Judah, Unbounded filters on $\omega$, in Stud. Logic Found. Math., 129,
North-Holland, Amsterdam, 1989, 105-115.
There exists a Sigma^1_2-filter not having the Baire property
if and only if there exists a real r such L[r] is unbounded.

Judah, Absoluteness for projective sets,
in Proceedings of the European Logic Colloquium, Helsinki, 1990.

Judah, $\Sigma^1_2$-sets of reals, JSL 53(1988) 636-642.

Judah, $\Delta^1_3$-Sets: measure and category, to appear in:
Set Theory of the Reals, Proceedings of Bar-Ilan Conference in
Honour of A.Fraenkel.

Judah-Shelah, Martin's axiom, measurability and equiconsistency results,
JSL 54(1989) 78-94.

Judah-Shelah, $\Delta^1_2$-sets of reals, APAL 42(1989) 207-233.

Judah-Shelah, $\Delta^1_3$-sets of reals,

Kechris, On a notion of smallness for subsets of the Baire space,
Trans AMS, 229(1977) 191-207.  Sigma_1^1 sets are K_sigma-regular.

Levy-Solovay, On the decomposition of sets of reals to Borel sets,
Ann of Math Logic, 5(1972) 1-19.

Louveau,$\sigma$-ideaux engendres par des ensembles fermes et theoremes
d'approximation, Trans AMS 257(1980) 143-169.  Every set is K_sigma-regular
in Solovay's model.

Raisonnier, A mathematical proof of S.Shelah's theorem on the measure
problem and related results, Israel J Math, 48(1984) 48-56.

Raisonnier-Stern, The strength of measurability hypotheses,
Israel J Math, 50(1985) 337-349.  Sigma^1_2(LM) -> Sigma^1_2(BP).

Shelah, Can you take Solovay's inaccessible away?, Israel J Math,
48(1984) 1-47.  Yes: Con(ZF)-> Con(ZF+DC+BP) and No:
LM-> omega_1 inacc in L.

Shelah, On measure and category, Israel J Math  52(1985) 110-114.
Con(ZF+DC+LM+notBP+notP)

Shelah-Woodin, Large cardinals imply that every reasonably
definable set of reals is Lebesgue measurable, Israel J Math, 70(1990)
381-394.  If there is a supercompact cardinal k, then L[R] is elementarily
equivalent to L[R] of V[G] where G is the Levy collapse of k.

Solovay, A model of set-theory in which ever set of reals is Lebesgue
measurable, Ann of Math, 92(1970) 1-56.

Stern, Generic extensions which do not add random reals, in Lecture Notes
in Math., 1130, Springer 1985, 395-407.
Con(ZF)-> Con( ZFC + Sigma^1_2(BP) + Sigma^1_2(R) )

Stern, Regularity properties of definable sets of reals,
Ann Pure Appl Logic, 29(1985) 289-324. Every set is K_sigma regular
also holds in Shelah's model.

Stern, On Lusin's restricted continuum problem, Ann of Math, 120(1984) 7-37.
In Solovay's model there is no equivalence relation on the reals such that
every equivalence class is Borel, there is a bound on the Borel rank of
equivalence classes, and there is no perfect set of pairwise
inequivalent elements.




                Proper forcing References
                  A. Miller May 92


Abraham, U., Shelah, S., Isomorphism types of Aronszajn trees,
Israel J. Math. 50 (1985),  75-113.

Abraham, Rubin, Shelah, On the consistency of some partition theorems
for the continuous colorings and the sturcture of omega1 dense
real order types, Annals of pure and applied logic, 29, 1985, 123-306.

Bekkali, M.,  Todorcevic, Stevo,  Topics in set theory,
Lecture Notes in Mathematics, 1476,  Springer-Verlag,  1991.

Beaudoin, Robert E., Strong analogues of Martin's axiom imply axiom R,
JSL 52 (1987), 216-218.

Beaudoin, Robert E., The proper forcing axiom and stationary set reflection,
Pacific J. Math. 149 (1991), 13-24.

Burger, Gerd,  The  Malitz quantifier theory of the class of Archimedian real
closed  fields,  Arch. Math. Logic, 28 (1989), 155-166.   PFA implies its a
decidable theory.

Balogh, Zoltan,  On compact Hausdorff spaces of countable tightness, PAMS
105 (1989), no. 3, 755--764. PFA implies every compact Hausdorff space
of countable tightness is sequential.

Balogh, Dow, Fremlin, Nyikos,  Countable tightness and proper forcing,
PAMS 19 (1988), no. 1, 295-298.

Baumgartner, James E.,  Applications of the proper forcing axiom,
Collection: Handbook of set-theoretic topology, 913-959 North-Holland, 1984.

Baumgartner, James E.,  Iterated forcing,  Collection: Surveys in set theory,
1-59,  London Math. Soc. Lecture Note Ser., 87,  1983  Cambridge Univ. Press.

Devlin, Keith J.,  The Yorkshireman's guide to proper forcing,
Collection: Surveys in set theory, 60-115, London Math. Soc. Lecture
Note Ser., 87,  1983,  Cambridge Univ. Press.

Devlin, Steprans, Watson, The number of directed sets,  Topology conference
(L'Aquila, 1983),  Rend. Circ. Mat. Palermo  1984, Suppl. No. 4, 31-41.

Dow, Alan, An introduction to applications of elementary submodels to
topology, Topology Proceedings 13 (1988),17-72.  (PFA) Each compact
space of countable tightness  contains points of  countable character.

Dow, Alan, PFA and uniform ultrafilters on omega1,
Top and its Apps, 28 (1988), 127-140.

Dow, Alan,  Simon, Petr,  Vaughan, Jerry E., Strong homology and the proper
forcing axiom, PAMS  106 (1989),  821-828.

Fleissner, William G., Left separated spaces with point-countable bases,
TAMS  294  (1986), 665-677.

Foreman, Magidor, Shelah, Martin's maximum, saturated ideals, and
nonregular ultrafilters I,  Ann. of Math. 127 (1988),  1-47.

Fremlin, D. H., Perfect pre-images of omega_1 and the PFA,
Topology and its Applications, 29 (1988), 151-166.

Gruenhage, Gary, Cosmicity of cometrizable spaces, TAMS 313 (1989), 301-315.
 X is cometrizable if there is a  weaker metrizable topology on X such
 that each point of X has a
 neighborhood base consisting of sets which are closed in the metric
 topology.  Under  PFA, if X is a cometrizable space with no uncountable
 discrete  subspaces, then either X is a continuous image of a separable
 metric space or X contains a copy of an  uncountable subspace of the
 Sorgenfrey line.

Jech, T., Multiple forcing, Cambridge Tracts in Mathematics 88, 1986.

Mekler, Alan H., Proper forcing and abelian groups,
Collection: Abelian group theory (Honolulu, Hawaii, 1983), 285-303
Lecture Notes in Math., 1006, Springer,  1983.

Mekler, Alan H., c.c.c. forcing without combinatorics. JSL 49 (1984), 830-832.

Miyamoto, Tadatoshi, c.c.c. * ctbly-closed vs. ctbly-closed * c.c.c.
Kobe J. Math.  6 (1989),  183-187.

Shelah, Saharon, More on proper forcing, JSL 49 (1984),  1034-1038.

Shelah, Saharon, Semiproper forcing axiom implies Martin maximum
but not PFA+, JSL 52 (1987), 360-367.

Shelah, Saharon, Steprans, Juris, PFA implies all automorphisms are
trivial, PAMS 104 (1988), 1220-1225.

Shelah,  Some notes on iterated forcing with c>omega2, Notre Dame J.
Formal Logic  29 (1988),  1-17.

Todorcevic, Stevo,  A note on the proper forcing axiom.
Collection: Axiomatic set theory (Boulder, Colo., 1983), 209-218
Contemp. Math., 31, AMS  1984.  (PFA) implies failure of squares.

Todorcevic, Stevo, Directed sets and cofinal types, TAMS 290 (1985), 711-723.

Todorcevic, Stevo, Partition problems in topology, Cont. Math., 84, AMS 1989.

Velickovic, Boban, CCC posets of perfect trees, Comp. Math. 79 (1991), 279-294.

Velickovic, Boban, Definable automorphisms of P(omega)/fin, PAMS 96
(1986) 130-135.

Velickovic, Boban, OCA and automorphisms of P(omega)/fin.

-----------------


Attending the course:

arratia-quesada argimiro
lamb david
letarte alan
nedervold eric
ortiz carlos
pruim randall
raw matt
ren jun
schwalm stephen
spasojevic zoran
wingers louis