There will be a Very Informal Gathering of
Logicians (VIG) at UCLA, from Friday,
January 30, to Sunday, February 1, 2015, the eighteenth in a series
of logic meetings at UCLA which started in 1976.
This VIG is organized to honor
Donald A. Martin
on the occasion of his formal retirement from UCLA.
It is partially supported by NSF Grant DMS 1463601.
Friday, January 30, in Young Hall CS76 (the Chemistry building)
across the Court of Sciences from
the Math building and Boelter Hall
3:00  3:30 
Pierre Simon,
Rosenthal compacta and NIP formulas.
A compact space is a Rosenthal compactum if it can be embedded
into the space of Baire class 1 functions on a Polish space.
Those objects have been well studied in functional analysis and
set theory. In this talk, I will explain the link between them
and the modeltheoretic notion of NIP and how they can be used to
prove new results in model theory on the topology of the space of
types.
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 Refreshments 
4:10  4:40 
Sherwood Hachtman,
Calibrating the strength of Borel
determinacy.
Infinite games with Borel payoff are determined, and this cannot
be proven without appeal to some form of the axioms of Replacement
and Power set. But what ambient set theory is strictly necessary?
In this talk, we isolate a family of reflection principles that
correspond exactly in strength to determinacy for certain levels
of the Borel hierarchy. We also discuss some connections with
measurable cardinals and higher order reverse mathematics.
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4:50  5:40 
Andrew Marks, Uniformly Turing invariant functions and
Borel combinatorics. 
6:00, Get together in MS 6627, the Math Department Lounge
Saturday, January 31, in IPAM (the Institute
for Pure and Applied Mathematics)
8:45  9:30 
Breakfast 
9:30  10:20 
W. Hugh Woodin, The form of UltimateL. 
10:30  11:20 
Stephen Jackson,
Forcing and combinatorial structure in Borel equivalence relations.
In the last several years there have been new methods introduced
into the theory of countable Borel equivalence relations which
have solved some problems which were previously not accessible.
These new methods center around an interplay between forcing
arguments and the combinatorial structure of the equivalence
relation. We will present a number of results along these lines,
including some very recent results. Interestingly, some of these
results for Z^d seem to be analogs of results by Marks for the
free groups, but the techniques seem to be completely different.
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11:30  12:20 
Sergei Starchenko,
Topological groups, mutypes and their stabilizers
(joint work with Y. Peterzil).
It is known that in $o$minimal structures, any unbounded definable
curve inside a definable group $G$ gives rise to a onedimensional
torsionfree definable subgroup of $G$, associated to the curve at
``infinity'' (a result of Peterzil and Steinhorn, 1999). In this
talk I will recall this construction and describe a
generalization of the result to definable types of arbitrary
dimension: Each definable type $p$ inside $G$ gives rise to a
definable, torsionfree subgroup $H_p$, whose dimension can be
readoff the type $p$.
As we will see, the group $H_p$ is the stabilizer of a partial type
associated to $p$, under the action of $G$ on a certain quotient of
the usual types space $S(G)$. It turns out that this quotient of
the type space is closely related to the classical construction
of Samuel’s compactification of topological groups and more
generally of spaces with uniformity.
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2:00  2:50 
The 2015 Hjorth Lecture,
Antonio Montalban, Vaught's conjecture and Computability Theory. 
 Refreshments 
3:30  4:20 
Charles Parsons, Concepts versus objects. 
4:30  5:20 
Kit Fine, The possibility of vagueness. 
5:30  6:20 
Katrin Tent,
Sharply 3transitive groups
.
The finite sharply 2 and 3transitive groups were classified
by Zassenhaus in the 1930 and all (but finitely many) arise
(essentially) from fields. It was an open question whether
the same is true in the infinite case. We answer this question.
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Evening party, details to be announced
Sunday, February 1, in IPAM (the Institute
for Pure and Applied Mathematics)
9:15  10:00 
Breakfast 
10:00  10:50 
Itay Neeman, Forcing on $\aleph_2$. 
11:00  11:30 
Anush Tserunyan,
A general van der Corput lemma and underlying Ramsey theory
.
A major theme in ergodic Ramsey theory is proving multiple
recurrence results for certain doubly recurrent (mixing) actions
of semigroups. The amplification of double to multiple recurrence
is usually done using a socalled van der Corput difference lemma
for a suitable filter on the semigroup. Particular instances of
this lemma (for concrete filters) have been proven before (by
Furstenberg, BergelsonMcCutcheon, and others), with a different
proof for each filter. We define a notion of differentiation for
subsets of semigroups and isolate the class of filters that
respect this notion. The filters in this class (call them
Deltafilters) include all of those for which the van der Corput
lemma was known, and our main result about them is a Ramsey
theorem related to labeling edges between the semigroup elements
with their ratios. An application of this theorem yields a van
der Corput lemma for Deltafilters, generalizing all its previous
instances.
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 Refreshments 
12:00  12:50 
John Steel, Some equiconsistencies at the level of subcompact
cardinals. 
