Monday, September 26, 2016

04:45 pm
- 06:00 pm

Logic Seminar

Philip Scowcroft, Wes: " Abelian
lattice-ordered groups with at most finitely many pairwise disjoint elements." Abstract : Conrads
characterization (1960) of the lattice-ordered groups with at most finitely
many pairwise disjoint elements yields model-completions for various theories
of such groups. A corresponding Nullstellensatz, and various
quantifier-elimination results, assume stronger forms when restricted to
special groups in the class.

Exley Science Center Tower ESC 638

Monday, November 09, 2015

04:45 pm
- 06:00 pm

Logic Seminar, Bill Calhoun (Bloomsburg University): "Triviality and lowness for K-reducibility and related reducibilities"

n 2 !,
where K is prefix-free Kolmogorov complexity. The set A is low
for K
if KA(y) = K(y)+O(1) for y 2 2<!. These definitions seem quite
different.
K-triviality indicates that initial segments of A have the lowest
possible
complexity, while lowness for K indicates that A is too weak as
an
oracle to reduce the complexity of any string. The remarkable equivalence
of
the two definitions was shown by Nies [2]. Replacing prefix-free
complexity
by monotone complexity in the definition of K-trivial, we obtain
the Km-trivial
sets. Every K-trivial set is Km-trivial and all Turing
degrees
_ 00 contain a Km-trivial set [1]. Yet, not every Turing degree
contains
a Km-trivial set. We obtain a superset of the Km-trivial sets by
defining
A to be almost-K-trivial if there is a real number a such that
K(A _
n) _+ aK(n). Every Km-trivial set is almost-K-trivial. However,
the
Turing degree of a computably dominated ML-random cannot contain
any
almost-K-trivial set. An interesting question is to determine
which
Turing degrees contain Km-trivial sets (or almost-K-trivial sets).
Recently,
this question has been considered for minimal Turing degrees.
We
also consider lowness for monotone and a priory complexity.
References
1.
Calhoun, W.C.: Triviality and minimality in the degrees of monotone complexity,
Journal
of Logic and Computation 22, 197-206 (2012).
2.
Nies, Andre: Lowness properties and randomness, Advances in Mathematics
197,
274-305 (2005).

Exley Science Center (Tower)

Monday, September 21, 2015

04:45 pm
- 06:00 pm

CT Logic Seminar, Vincent Guingona (Wes): "A Local Characterization of VC-Minimality"

Abstract :
( Joint work with Uri Andrews ) This talk is in the intersection of
computable model theory and neostability theory. I discuss VC-minimality,
a model-theoretic notion of complexity for theories that generalizes
o-minimality and is generalized by dp-minimality and NIP. Unlike
o-minimality and dp-minimality, a priori , it is difficult to
determine if a given theory is VC-minimal. In computability terms, the
definition of VC-minimality, in its original form, is Sigma_1^1. However,
my coauthor and I show that VC-minimality is, in fact, Pi^0_4-complete by
giving a local characterization (for countable languages). This leads to
a list of examples of theories whose VC-minimality is determined.

Exley Science Center (Tower)

Monday, September 14, 2015

04:45 pm
- 05:45 pm

Logic Seminar, Reed Solomon (UConn): "Strong reducibilities, RT^1_3 and SRT^2_2"

Abstract: Various
strong reductions between Pi^1_2 principles have been used in recent years to
shed light on difficult problems in reverse mathematics. I will introduce some
of these reductions and discuss their connection to reverse math. The main
theorem of the talk is that RT^1_3 is not strongly computably reducible to
SRT^2_2. This result is joint work with Damir Dzhafarov, Ludovic Patey and
Linda Brown Westrick.

Monday, April 27, 2015

04:45 pm
- 06:00 pm

Logic Seminar, Petr Glivicky (Charles University): 'Definability in linear fragments of Peano Arithmetic'

Abstract: In this talk, I will give an overview of recent results on linear arithmetics with main focus on definability in their models. Here, for a cardinal k, the k-linear arithmetic (LAk) is a full-induction arithmetical theory extending Presburger arithmetic by k non-standard scalars (= unary functions of multiplication by distinguished elements). The hierarchy of linear arithmetics lies between Presburger and Peano arithmetics and stretches from tame to wild. I will present a quantifier elimination result for LA1 and give a complete characterisation of definable sets in its models. On the other hand, I will construct an example of a model of LA2 (or any LAk with k at least 2) where multiplication is definable on a non-standard initial segment (and thus no similar quantifier elimination is possible). There is a close connection between models of linear arithmetics and certain discretely ordered modules (as each model of a linear arithmetic naturally corresponds to a discretely ordered module over the ordered ring generated by the scalars) which allows to construct wild (e.g. non-NIP) ordered modules. On the other hand, the quantifier elimination result for LA1 implies interesting properties of the structure of saturated models of Peano arithmetic.

ESC 638

Monday, March 30, 2015

04:45 pm
- 06:00 pm

Logic Seminar, Reed Solomon (UConn): 'Revisiting EM and ADS'

Abstract: In this talk, I will present recent work by Ludovic Patey which simplifies and extends the proof that the Erdos-Moser principle (that every infinite tournament has an infinite transitive sub tournament) does not imply ADS (that every linear order contains either an infinite ascending sequence or an infinite descending sequence).

ESC 638

Tuesday, March 24, 2015

04:15 pm
- 05:30 pm

Computer Science Seminar, Marc Liberatore (UMass): 'BitCoin: WTF is it, and is it really anonymous?'

Abstract: In this talk, we'll (re-)develop the BitCoin protocol step-by-step. We'll start with a simple centralized service for digital cash, and end up with a sketch of the distributed consensus system that we all love -- or love to hate. We will briefly survey the state of BitCoin and related systems, with a focus on how much privacy they really provide to their users. Then, we'll present the problem of mixing BitCoin to increase user privacy. We will see that centralized mix systems based on protocols like CoinJoin have the same problems found in centralized proxies for general communications, and more besides. We'll show that the Sybil attack is one such problem -- a critical one -- and present Xim, our distributed approach to Sybil-resistant matchmaking.(While this talk will be technical, you won't need a deep knowledge of cryptography or protocols to follow it. My goal is for undergraduate liberal arts majors with some math or computer science background to be comfortable in following along and in asking questions as they come up.)Marc Liberatore is a research scientist and occasional lecturer in the School of Computer Science at the University of Massachusetts Amherst, and the associate director of the Center for Forensics at UMass. Prior to his current appointment, he was a Mellon Fellow and Visiting Assistant Professor at Wesleyan University. His research interests include network, cellular, and filesystem forensics, anonymous communication systems, and peer-to-peer architectures.

ESC 638

Tuesday, March 24, 2015

04:15 pm
- 05:30 pm

Computer Science Seminar, Marc Liberatore (UMass): 'BitCoin: WTF is it, and is it really anonymous?'

Abstract: In this talk, we'll (re-)develop the BitCoin protocol step-by-step. We'll start with a simple centralized service for digital cash, and end up with a sketch of the distributed consensus system that we all love -- or love to hate. We will briefly survey the state of BitCoin and related systems, with a focus on how much privacy they really provide to their users. Then, we'll present the problem of mixing BitCoin to increase user privacy. We will see that centralized mix systems based on protocols like CoinJoin have the same problems found in centralized proxies for general communications, and more besides. We'll show that the Sybil attack is one such problem -- a critical one -- and present Xim, our distributed approach to Sybil-resistant matchmaking. (While this talk will be technical, you won't need a deep knowledge of cryptography or protocols to follow it. My goal is for undergraduate liberal arts majors with some math or computer science background to be comfortable in following along and in asking questions as they come up.) Marc Liberatore is a research scientist and occasional lecturer in the School of Computer Science at the University of Massachusetts Amherst, and the associate director of the Center for Forensics at UMass. Prior to his current appointment, he was a Mellon Fellow and Visiting Assistant Professor at Wesleyan University. His research interests include network, cellular, and filesystem forensics, anonymous communication systems, and peer-to-peer architectures.

ESC 638

Monday, March 23, 2015

04:45 pm
- 06:00 pm

Logic Seminar, Stephen Flood (UConn): 'Separating Decomposability and Tree- Decomposability'

Abstract: The theory of graph decompositions studies the infinite graphs that can be built using a sequence of irreducible graphs which are pasted together at complete subgraphs. In this theory, there are several combinatorial characterizations of the tree-decomposable graphs, but a combinatorial characterization of general decomposable graphs has proved elusive.In this talk, we approach this question from the perspective of mathematical logic. We show that there is indeed a difference between characterizing decomposable and tree-decomposable graphs. More precisely, we show that the index set of computable decomposable graphs is $\Pi^1_1$ hard and $\Sigma^1_2$ definable, whereas the index set of computable tree-decomposable graphs is $\Sigma^1_1$ definable.

ESC 638

Monday, November 17, 2014

04:45 pm
- 06:00 pm

CT Logic Seminar, Linda Brown Westrick (UConn): 'Effective Dimension in Subshifts'

Abstract: A subshift is a subset of Cantor space that is both topologically closed and closed under the shift operation. Any element of a subshift can be viewed as a trajectory in a discrete dynamical system. One way a trajectory can be complicated is to have a large effective dimension. We consider the effective dimension spectrum of a subshift X, defined as {dim x : x in X}, where dim is the effective dimension. Most commonly, the dimension spectrum of X is [0,h(X)], where h(X) is the entropy of X. We give examples where the dimension spectrum does not follow this pattern, and discuss partial results and open questions related to the problem of characterizing the dimension spectra of subshifts. No prior knowledge about subshifts will be assumed.

ESC 638

Monday, November 10, 2014

04:45 pm
- 06:00 pm

CT Logic Seminar, Gwyneth Harrison-Shermoen (Wes): 'Independence, via limits'

Abstract: Given a large model $M$ of some theory $T$, I will describe a method for lifting well-behaved notions of independence from the theories of substructures of $M$ to a reasonably well-behaved notion of independence in $M$. (In essence, we take the limit of the independence relations in the substructures.) The motivating example - two-sorted theories of infinite-dimensional vector spaces over an algebraically closed field and with a bilinear form - was worked out by N. Granger in his thesis. I will outline this example before launching into the more general framework.

ESC 638

Monday, October 27, 2014

04:45 pm
- 06:00 pm

CT Logic Seminar, Cameron Hill (Wes): 'Some Remarks on Certain 0,1-Laws'

Abstract: I will begin by reminding everyone what a Fra\iss\e class is, and I will introduce a certain family of ultrafilters related to such a class. After that, I will review what is (usually) intended when one says that a Fra\iss\e class has a 0,1-law for first-order sentences. Finally, I will propose a method of indexing asymptotic distributions on a Fra\iss\e class by elements of a certain compact space, and I will discuss some results that can be proved using this method.

ESC 638

Monday, September 15, 2014

04:45 pm
- 06:00 pm

CT Logic Seminar, Philip Scowcroft (Wes): 'Continuous Model Theory for C(X)'

Abstract: In the continuous logic recently developed by Ben Yaacov and others, the class of lattice-ordered groups isomorphic to C(X) with X compact is an elementary class. The theory T of this class has convenient model-theoretic properties: for example, T has a model-completion T(+) which is countably categorical and admits elimination of quantifiers. One may establish also a corresponding Nullstellensatz and determine which models of T have prime-model extensions to models of T(+).

ESC 638

Monday, January 20, 2014

04:45 pm
- 06:00 pm

Logic Seminar, Neil Immerman (UMass): 'Descriptive and Dynamic Complexity'

Abstract: An increasing percentage of modern computation is dynamic: a fairly large object is being worked on over a period of time. The object is repeatedly modified and computations are performed. Using auxiliary data structures we can sometimes maintain the ability to very quickly answer certain queries about the object as it changes. dynFO is the set of properties that can be maintained and queried in First-Order logic. Much progress has been made understanding when graph reachability is in dynFO and related classes, but the general question remains open.

ESC 638

Monday, November 25, 2013

04:45 pm
- 06:00 pm

Logic Seminar, Philip Scowcroft (Wesleyan): ' Existentially closed prime-model extensions of Abelian lattice-ordered groups.'

Abstract: Existentially closed (ec) Abelian lattice-ordered groups are to Abelian lattice-ordered (l-) groups as algebraically closed fields are to fields. An ec prime-model extension of the Abelian l-group G is an ec Abelian l-group that extends G and embeds over G into any ec Abelian l-group extending G. So the Abelian l-group G is to an ec prime-model extension of G as a field F is to its algebraic closure. This talk will consider the extent to which Abelian l-groups have ec prime-model extensions.

ESC 638

Monday, October 21, 2013

04:45 pm
- 05:45 pm

Logic Seminar, Lynn Scow (Vassar): 'Ramsey transfer theorems'

Abstract: We survey some of the known approaches to transfer a Ramsey theorem for one class of finite structures to another. We will isolate some easy consequences and point to further directions.

ESC 638

Monday, October 14, 2013

04:45 pm
- 05:45 pm

LogicSeminar, Henry Towsner (Univeristy of Pennsylvania): 'Models of Reverse Mathematics'

Abstract: Most recent work in reverse mathematics has focused on the consequences of Pi12 sentences. One family of questions asks, given a Pi12 sentence, what its first-order consequences are---what the Pi12 sentence implies about the underlying first-order model of arithmetic. Turning this around, once we have a theory of reverse mathematics, we can ask about the collection of all Pi12 sentences which are conservative over it for first-order consequences. When our theory T is the theory ACA0 (or, in fact, any computably axiomatized theory containing ACA0), the collection of such sentences is as complicated as possible their Godel numbers form a Pi02 complete set). Over weaker theories, however, the method of proof fails. We show that for the most important class of weaker theories, those of the form RCA0 plus Sigma_n induction for some n, the same result holds. Our method is completely different than the proof for ACA0, and has the side benefit of sharply constraining what the theories RCA0+ISigma_n can prove about formulas more complicated than ISigma_n.

ESC 638

Monday, October 07, 2013

04:45 pm
- 06:00 pm

Logic Seminar, Russell Miller (Queens College, CUNY): 'Fields and Computable Categoricity'

Abstract: We give an overview of the current understanding of computable categoricity for fields. A computable field F is computably categorical if, for every computable field E which is isomorphic to F (via any isomorphism), there exists a computable isomorphism from E onto F. Characterizations of computable categoricity are known for various other classes of computable structures, and for certain subclasses of computable fields, but have proven elusive for fields. We give an analysis of the reasons why, considering both the complexity of the definition of computable categoricity and the amount of information needed to compute field isomorphisms when they exist.

ESC 638