863 research outputs found
Symmetries and Ramsey properties of trees
AbstractIn this paper we show the extent to which a finite tree of fixed height is a Ramsey object in the class of trees of the same height can be measured by its symmetry group
Techniques for approaching the dual Ramsey property in the projective hierarchy
We define the dualizations of objects and concepts which are essential for
investigating the Ramsey property in the first levels of the projective
hierarchy, prove a forcing equivalence theorem for dual Mathias forcing and
dual Laver forcing, and show that the Harrington-Kechris techniques for proving
the Ramsey property from determinacy work in the dualized case as well
Permutations on the random permutation
The random permutation is the Fra\"iss\'e limit of the class of finite
structures with two linear orders. Answering a problem stated by Peter Cameron
in 2002, we use a recent Ramsey-theoretic technique to show that there exist
precisely 39 closed supergroups of the automorphism group of the random
permutation, and thereby expose all symmetries of this structure. Equivalently,
we classify all structures which have a first-order definition in the random
permutation.Comment: 18 page
Ramseyan ultrafilters
We investigate families of partitions of omega which are related to special
coideals, so-called happy families, and give a dual form of Ramsey ultrafilters
in terms of partitions. The combinatorial properties of these
partition-ultrafilters, which we call Ramseyan ultrafilters, are similar to
those of Ramsey ultrafilters. For example it will be shown that dual Mathias
forcing restricted to a Ramseyan ultrafilter has the same features as Mathias
forcing restricted to a Ramsey ultrafilter. Further we introduce an ordering on
the set of partition-filters and consider the dual form of some cardinal
characteristics of the continuum
The Ramsey Theory of Henson graphs
Analogues of Ramsey's Theorem for infinite structures such as the rationals
or the Rado graph have been known for some time. In this context, one looks for
optimal bounds, called degrees, for the number of colors in an isomorphic
substructure rather than one color, as that is often impossible. Such theorems
for Henson graphs however remained elusive, due to lack of techniques for
handling forbidden cliques. Building on the author's recent result for the
triangle-free Henson graph, we prove that for each , the
-clique-free Henson graph has finite big Ramsey degrees, the appropriate
analogue of Ramsey's Theorem.
We develop a method for coding copies of Henson graphs into a new class of
trees, called strong coding trees, and prove Ramsey theorems for these trees
which are applied to deduce finite big Ramsey degrees. The approach here
provides a general methodology opening further study of big Ramsey degrees for
ultrahomogeneous structures. The results have bearing on topological dynamics
via work of Kechris, Pestov, and Todorcevic and of Zucker.Comment: 75 pages. Substantial revisions in the presentation. Submitte
NCUWM Talk Abstracts 2010
Dr. Bryna Kra, Northwestern University
“From Ramsey Theory to Dynamical
Systems and Back”
Dr. Karen Vogtmann, Cornell University
“Ping-Pong in Outer Space”
Lindsay Baun, College of St. Benedict
Danica Belanus, University of North Dakota
Hayley Belli, University of Oregon
Tiffany Bradford, Saint Francis University
Kathryn Bryant, Northern Arizona University
Laura Buggy, College of St. Benedict
Katharina Carella, Ithaca College
Kathleen Carroll, Wheaton College
Elizabeth Collins-Wildman, Carleton College
Rebecca Dorff, Brigham Young University
Melisa Emory, University of Nebraska at Omaha
Avis Foster, George Mason University
Xiaojing Fu, Clarkson University
Jennifer Garbett, Kenyon College
Nicki Gaswick, University of Nebraska-Lincoln
Rita Gnizak, Fort Hays State University
Kailee Gray, University of South Dakota
Samantha Hilker, Sam Houston State University
Ruthi Hortsch, University of Michigan
Jennifer Iglesias, Harvey Mudd College
Laura Janssen, University of Nebraska-Lincoln
Laney Kuenzel, Stanford University
Ellen Le, Pomona College
Thu Le, University of the South
Shauna Leonard, Arkansas State University
Tova Lindberg, Bethany Lutheran College
Lisa Moats, Concordia College
Kaitlyn McConville, Westminster College
Jillian Neeley, Ithaca College
Marlene Ouayoro, George Mason University
Kelsey Quarton, Bradley University
Brooke Quisenberry, Hope College
Hannah Ross, Kenyon College
Karla Schommer, College of St. Benedict
Rebecca Scofield, University of Iowa
April Scudere, Westminster College
Natalie Sheils, Seattle University
Kaitlin Speer, Baylor University
Meredith Stevenson, Murray State University
Kiri Sunde, University of North Carolina
Kaylee Sutton, John Carroll University
Frances Tirado, University of Florida
Anna Tracy, University of the South
Kelsey Uherka, Morningside College
Danielle Wheeler, Coe College
Lindsay Willett, Grove City College
Heather Williamson, Rice University
Chengcheng Yang, Rice University
Jie Zeng, Michigan Technological Universit
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