% LaTex2e
\documentclass[12pt]{article}
\usepackage{amssymb,latexsym}

\begin{document}

\begin{center}
Some references on wqo, bqo, scattered types, Fraisse conjecture.\\
A.Miller \\
Fall 2006 \\
\today
\end{center}

\bigskip\bigskip

Abraham, Uri; Bonnet, Robert Hausdorff's theorem for posets that satisfy the
finite antichain property.  Fund. Math.  159  (1999),  no. 1, 51--69.
Generalizes Hausdorff's hierarchy of scattered linear order types.

Argyros, Spiros A.; Todorcevic, Stevo Ramsey methods in analysis. Advanced
Courses in Mathematics. CRM Barcelona. Birkhauser Verlag, Basel, 2005. viii+257
pp. ISBN: 978-3-7643-7264-4; 3-7643-7264-8
Todorcevic surveys bqo theory.

Bonnet, Robert; Rubin, M. Elementary embedding between
countable Boolean algebras. J. Symbolic Logic 56 (1991), no. 4, 1212--1229.
Countable models of a complete theory of boolean algebras are
wqo under elementary embeddability.

Cholak, Peter; Marcone, Alberto; Solomon, Reed Reverse mathematics and the
equivalence of definitions for well and better quasi-orders.  J. Symbolic
Logic  69  (2004),  no. 3, 683--712.

Clote, P. The metamathematics of scattered linear orderings.  Arch. Math.
Logic  29  (1989),  no. 1, 9--20.

Clote, P. The metamathematics of Fraisse's order type conjecture.  Recursion
theory week (Oberwolfach, 1989),  41--56, Lecture Notes in Math., 1432,
Springer, Berlin, 1990.

Corominas, E. On better quasi-ordering countable trees. Special volume on
ordered sets and their applications (L'Arbresle, 1982).  Discrete Math.  53
(1985), 35--53.

Diestel, Reinhard Relating subsets of a poset, and a partition theorem for
WQOs. Order 18 (2001), no. 3, 275--279.

Duparc, J. The Steel hierarchy of ordinal valued Borel mappings.  J. Symbolic
Logic  68  (2003),  no. 1, 187--234.

Dzamonja, Mirna; Thompson, Katherine A poset hierarchy.  Cent. Eur. J. Math.
4 (2006),  no. 2, 225--241.  Generalizes Abraham-Bonnet (1999).

E.Ellentuck, A new proof that analytic sets are Ramsey, J. Symbolic Logic,
39(1974),163-165.

van Engelen, Fons; Miller, Arnold W.; Steel, John Rigid Borel sets and better
quasi-order theory. Logic and combinatorics (Arcata, Calif., 1985), 199--222,
Contemp. Math., 65, Amer. Math. Soc., Providence, RI, 1987.

Fra\"iss\'e, Roland Theory of relations. Revised edition. With an appendix by
Norbert Sauer. Studies in Logic and the Foundations of Mathematics, 145.
North-Holland Publishing Co., Amsterdam, 2000. ii+451 pp. ISBN: 0-444-50542-3
Revised version contains bqo theory.

Friedman, Harvey; Robertson, Neil; Seymour, Paul The metamathematics of the
graph minor theorem.  Logic and combinatorics (Arcata, Calif., 1985),
229--261, Contemp. Math., 65, Amer. Math. Soc., Providence, RI, 1987.

Friedman, Harvey M. Internal finite tree embeddings.  Reflections on the
foundations of mathematics (Stanford, CA, 1998),  60--91, Lect. Notes Log., 15,
Assoc. Symbol. Logic, Urbana, IL, 2002.

F.Galvin and K.Prikry, Borel sets and Ramsey's theorem, J. Symbolic Logic,
(1973)38, 193-198.

Hausdorff, F.; Grundzuge einer Theorie der geordneten Mengen. (German)  Math.
Ann.  65  (1908),  no. 4, 435--505.  Hierarchy of scattered linear orders.

Haussler, David Another generalization of Higman's well-quasi-order result on
$\Sigma\sp *$. Discrete Math. 57 (1985), no. 3, 237--243.

Jancar, Petr A note on well quasi-orderings for powersets.  Inform. Process.
Lett.  72  (1999),  no. 5-6, 155--160.

Jenkyns, T. A.; Nash-Williams, C. St. J. A. Counterexamples in the theory of
well-quasi-ordered sets. 1969  Proof Techniques in Graph Theory (Proc. Second
Ann Arbor Graph Theory Conf., Ann Arbor, Mich., 1968)  pp. 87--91 Academic
Press, New York

Kríz, Igor Proving a witness lemma in better-quasiordering theory: the method
of "extensions".  Math. Proc. Cambridge Philos. Soc.  106  (1989),  no. 2,
253--262.

Kríz, Igor Well-quasiordering finite trees with gap-condition. Proof of
Harvey Friedman's conjecture.  Ann. of Math. (2)  130  (1989),  no. 1,
215--226.

Kriz, Igor; Thomas, Robin On well-quasi-ordering finite structures with
labels.  Graphs Combin.  6  (1990),  no. 1, 41--49.

Kriz, Igor; Thomas, Robin Ordinal types in Ramsey theory and
well-partial-ordering theory.  Mathematics of Ramsey theory,  57--95,
Algorithms Combin., 5, Springer, Berlin, 1990.

Kriz, Igor; Sgall, Jiri Well-quasiordering depends on the labels.
Acta Sci. Math. (Szeged)  55  (1991),  no. 1-2, 59--65.

Kriz, Igor; Thomas, Robin Analyzing Nash-Williams' partition theorem by
means of ordinal types. Directions in infinite graph theory and combinatorics
(Cambridge, 1989).  Discrete Math.  95  (1991),  no. 1-3, 135--167.

Kriz, Igor The structure of infinite Friedman trees.  Adv. Math.  115
(1995),  no. 1, 141--199.

Kruskal, Joseph B. The theory of well-quasi-ordering: A frequently discovered
concept.  J. Combinatorial Theory Ser. A  13  (1972), 297--305.

Kruskal, J. B. Well-quasi-ordering, the Tree Theorem, and Vazsonyi's
conjecture.  Trans. Amer. Math. Soc.  95  1960 210--225.

Kuhn, Daniela On well-quasi-ordering infinite trees - Nash-Williams's theorem
revisited.  Math. Proc. Cambridge Philos. Soc.  130  (2001),  no. 3, 401--408.

Landraitis, Charles K. Definability in well quasi-ordered sets of structures.
J. Symbolic Logic 42 (1977), no. 2, 289--291.

Landraitis, Charles A combinatorial property of the homomorphism relation
between countable order types.  J. Symbolic Logic  44  (1979), no. 3, 403--411.

Laver, Richard On Fra\"iss\'e's order type conjecture. Ann. of Math. (2) 93
1971 89--111.

Laver, Richard An order type decomposition theorem.  Ann. of Math. (2)  98
(1973), 96--119.

Laver, Richard Well-quasi-orderings and sets of finite sequences.  Math. Proc.
Cambridge Philos. Soc.  79  (1976), no. 1, 1--10. First section surveys
wqo theory.

Laver, Richard Better-quasi-orderings and a class of trees.  Studies in
foundations and combinatorics,  pp. 31--48, Adv. in Math. Suppl. Stud., 1,
Academic Press, New York-London, 1978.

Louveau, Alain; Simpson, Stephen G. A separable image theorem for Ramsey
mappings.  Bull. Acad. Polon. Sci. Sér. Sci. Math.  30  (1982), no. 3-4,
105--108.

Louveau, Alain(F-PARIS6-E); Saint-Raymond, Jean(F-PARIS6-E)
On the quasi-ordering of Borel linear orders under embeddability.
J. Symbolic Logic 55 (1990), no. 2, 537--560.

Mathias, A. R. D. Happy families.  Ann. Math. Logic  12  (1977), no. 1,
59--111.

Marcone, Alberto Borel quasi-orderings in subsystems of second-order
arithmetic. Ann. Pure Appl. Logic 54 (1991), no. 3, 265--291.

Marcone, Alberto Foundations of BQO theory.  Trans. Amer. Math. Soc.  345
(1994),  no. 2, 641--660.

Marcone, Alberto The set of better quasi orderings is
$\Pi\sb 2\sp 1$.  Math. Logic Quart.  41  (1995),  no. 3, 373--383.

Marcone, Alberto On the logical strength of Nash-Williams' theorem on
transfinite sequences.  Logic: from foundations to applications (Staffordshire,
1993),  327--351, Oxford Sci. Publ., Oxford Univ. Press, New York, 1996.

Marcone, Alberto Fine analysis of the quasi-orderings on the power set.  Order
18  (2001),  no. 4, 339--347 (2002).

Marcone, Alberto Wqo and bqo theory in subsystems of second order arithmetic.
Reverse mathematics 2001,  303--330, Lect. Notes Log., 21, Assoc. Symbol.
Logic, La Jolla, CA, 2005.

Mekler, Alan H. Scattered subsets of $Q$.  Order  9  (1992),  no. 2, 159--162.

Milner, E. C. Basic wqo- and bqo-theory. Graphs and order (Banff, Alta., 1984),
487--502, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 147, Reidel, Dordrecht,
1985.

Montalban, Antonio Up to equimorphism, hyperarithmetic is recursive.  J.
Symbolic Logic  70  (2005),  no. 2, 360--378.

Montalban, Antonio Equivalence between Fraisse's conjecture and Jullien's
theorem.  Ann. Pure Appl. Logic  139  (2006),  no. 1-3, 1--42.

Moore, J.  Structural analysis of Aronszajn trees,  to appear in the
Proceedings of the 2005 Logic Colloquium in Athens, Greece.
eprint 9-06 \par\noindent math.boisestate.edu/$\sim$justin/preprints.html
Question: Are Aronszajn lines under embeddability wqo?

Nash-Williams, C. St. J. A. On well-quasi-ordering trees. 1967  A seminar on
Graph Theory  pp. 79--82 Holt, Rinehart and Winston, New York.  Short
proof of Kruskal's Theorem.

Nash-Williams, C. St. J. A. On well-quasi-ordering infinite trees.  Proc.
Cambridge Philos. Soc.  61  1965 697--720.

Nash-Williams, C. St. J. A. On well-quasi-ordering transfinite sequences.
Proc. Cambridge Philos. Soc.  61  1965 33--39.  Sequences with finite
range.  Clopen sets are Ramsey.

Nash-Williams, C. St. J. A. On better-quasi-ordering transfinite sequences.
Proc. Cambridge Philos. Soc. 64 1968 273--290.

Pouzet, Maurice Sur les premeilleurordres. (French)  Ann. Inst. Fourier
(Grenoble)  22  (1972), no. 2, 1--19. $Q$ is bqo iff $Q^{<\omega_1}$ is
wqo.

Pouzet, Maurice; Sobrani, Mohamed The order type of the collection of finite
series-parallel posets.  Discrete Math.  265  (2003),  no. 1-3, 189--211.

Pr\"omel, Hans J\"urgen(D-BONN-DM); Voigt, Bernd(D-BLF) From wqo to bqo, via
Ellentuck's theorem. (English. English summary) Topological, algebraical and
combinatorial structures. Frol\'ik's memorial volume. Discrete Math. 108
(1992), no. 1-3, 83--106.

Rado, R. Partial well-ordering of sets of vectors. Mathematika 1, (1954).
89--95.

Rado, R., Erd\"os, P.;  A theorem on partial well-ordering of sets of vectors.
J. London Math. Soc.  34  1959 222--224.

Robertson, Neil; Seymour, P. D. Graph minors. XX. Wagner's conjecture.  J.
Combin. Theory Ser. B  92  (2004),  no. 2, 325--357.

Rosenstein, Joseph G. Linear orderings. Pure and Applied Mathematics, 98.
Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London,
1982. xvii+487 pp. ISBN: 0-12-597680-1

H.Rosenthal, A characterization of Banach spaces containing $l_1$, Proceedings
of the National Academy of Sciences (USA), 71(1974), 2411-2413.  Uses
Galvin-Prikry Theorem.

J.Silver, Every analytic set is Ramsey, JSL 35(1970), 60-64.

Simpson, Steven BQO Theory and Fraisse's conjecture in: \par\noindent
Mansfield, Richard; Weitkamp, Galen Recursive aspects of descriptive set
theory. With a chapter by Stephen Simpson. Oxford Logic Guides, 11. The
Clarendon Press, Oxford University Press, New York, 1985. vii+144 pp. ISBN:
0-19-503602-6.

Simpson, Steven Nonprovability of certain combinatorial properties of finite
trees.  Harvey Friedman's research on the foundations of mathematics,  87--117,
Stud. Logic Found. Math., 117, North-Holland, Amsterdam, 1985.

Smory\'nski, C. The varieties of arboreal experience.  Math. Intelligencer  4
(1982), no. 4, 182--189.  Friedman's finite version of Kruskal's Theorem
is not provable in Peano arithmetic.

Thomas, Robin A counterexample to "Wagner's conjecture" for infinite graphs.
Math. Proc. Cambridge Philos. Soc.  103  (1988),  no. 1, 55--57.

Thomas, Robin Well-quasi-ordering infinite graphs with forbidden finite planar
minor.  Trans. Amer. Math. Soc.  312  (1989),  no. 1, 279--313.

Thomass\'e, St\'ephan On better-quasi-ordering countable series-parallel
orders.  Trans. Amer. Math. Soc.  352  (2000),  no. 6, 2491--2505.
Series-parallel means that the letter Z poset does not embed.

Todorcevic, S. Lipschitz maps on trees, report no. 13, 2000/2001 Institut
Mittag-Leffler.  (Eric has 5 MB pdf file) Shows there is an uncountable
antichain of Aronszajn trees under tree embedability.

Wolk, E. S. Partially well ordered sets and partial ordinals. Fund. Math. 60
1967 175--186.  Equivalents of wqo.

\end{document}
