## Frank Tall: Co-analytic spaces, K-analytic spaces, and definable versions of Menger’s conjecture

Place: Fields Institute (Room 210)

Date: February 23 , 2018 (13:30-15:00)

Speaker: Frank Tall

Title: Co-analytic spaces, K-analytic spaces, and definable versions of Menger’s conjecture

Abstract: We continue the study of K-analytic and related spaces started last time, especially the connections between descriptive set theory as presented by Rogers and Jayne, and generalized metric spaces. We shall mention a number of unsolved problems and also give applications to productively Lindelof spaces and to topological groups.

## Sibylle Schwarz: Many-valued logic, Automata and Languages

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 21 February 2018, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Sibylle Schwarz

Title: Many-valued logic, Automata and Languages.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:
In 1960, Buechi, Elgot, Trakhtenbrot discovered a correspondence
between finite automata and monadic second order logic on words:
A language of nonempty words is regular if and only if it is
MSO-definable. Many-valued logics with truth values from MV-algebras
and weighted automata with weights from semirings are generalizations
of classical two-valued logics and finite automata, respectively.
In this talk, I give some examples of corresponding MV-algebras
and semirings and present translations between many-valued
MSO-formulae and weighted automata that define the same language.

## James Cummings: Some strong chain conditions

Mathematical logic seminar – Feb 20 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         James Cummings
Department of Mathematical Sciences
CMU

Title:     Some strong chain conditions

Abstract:

One of the basic facts in forcing is that a finite support iteration of ccc forcing is ccc. This underlies (for example) the consistency proof for Martin’s Axiom. In general an iteration of κ-closed κ+-cc forcing with <κ-support fails to be κ+-cc, and we need strngthened forms of the chain condition. I will discuss some of these strong chain conditions and the corresponding iteration theorems.

## Chris Kapulkin: Homotopy Type Theory and internal languages of higher categories

Thursday, February 22, 2018, from 4 to 5:30pm
East Hall, room 3088

Speaker: Chris Kapulkin (University of Western Ontario)

Title: Homotopy Type Theory and internal languages of higher categories

Abstract:

Homotopy Type Theory (or HoTT) is an approach to foundations of mathematics, building on the homotopy-theoretic interpretation of type theory. In addition to its foundational role, HoTT has been speculated to be the internal language of higher toposes in the sense of Joyal and Lurie.
This talk will be an introduction to HoTT, explaining its main ideas and presenting one way in which the connection between type theory and higher categories can be made precise.

## Will Brian: Autohomeomorphisms of ω∗ : the quotient relation

Place: Fields Institute (Room 210)

Date: February 16, 2018 (13:30-15:00)

Speaker: Will Brian

Title: Autohomeomorphisms of ω∗ : the quotient relation

Abstract: Given two autohomeomorphisms f and g of N*, we say that f is a quotient of g when there is a continuous surjection Q from N* to N* such that Qg = fQ. In other words, f is a quotient of g if it is the “continuous image” of g, in the appropriate sense.

I have been investigating this relation, and will present some of the results of that investigation in my talk. For example, under CH: there are many universal autohomeomorphisms (an autohomeomorphism is universal if everything else is a quotient of it); the quotient relation has uncountable chains and antichains; there is an exact description of the quotients of a given trivial map. Under OCA+MA the picture is still murky: for example, there is a jointly universal pair of autohomeomorphisms (meaning everything else is a quotient of one or the other), but I do not know if there is a single universal automorphism. I will sketch some of these results and include several open questions.

## BLAST 2018, Denver, August 6-10, 2018

BLAST 2018
August 6-10, 2018

The tenth-anniversary installment of BLAST will be held at the University of Denver from August 6 to August 10, 2018.

Tutorial speakers:

• Paul Gartside (University of Pittsburgh)
• George Metcalfe (Universität Bern)
• Drew Moshier (Chapman University)

Plenary speakers:

• Dana Bartosova (Carnegie Mellon University)
• Manuela Busaniche (National Scientific and Technical Research Council, Buenos Aires)
• Mirna Dzamonja (University of East Anglia, UK)
• David Fernandez-Breton (University of Michigan)
• Wesley Holliday (UC Berkeley)
• Agnes Szendrei (CU Boulder)

Local organizing committee:

• Natasha Dobrinen
• Wesley Fussner
• Nick Galatos
• Dan Hathaway
• Gavin St. John

Program committee:

• Natasha Dobrinen (Chair)
• Nick Galatos

## Rick Statman: Completeness of BCD for an operational semantics; forcing for proof theorists

Mathematical logic seminar – Feb 13 2018
Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Rick Statman
Department of Mathematical Sciences
CMU

Title: Completeness of BCD for an operational semantics; forcing for proof theorists

Abstract:

Intersection types provide a type discipline for untyped λ-calculus. The formal theory for assigning intersection types to lambda terms is BCD (Barendregt, Coppo, and Dezani). We show that BCD is complete for a natural operational semantics. The proof uses a primitive forcing construction based on Beth models (similar to Kripke models).

## Zach Norwood: Coding along trees and remarkable cardinals

Time: Mon, 02/12/2018 – 4:00pm – 5:30pm
Location: RH 440R

Speaker: Zach Norwood (UCLA)

Title: Coding along trees and remarkable cardinals

Abstract. A major project in set theory aims to explore the connection between large cardinals and so-called generic absoluteness principles, which assert that forcing notions from a certain class cannot change the truth value of (projective, for instance) statements about the real numbers. For example, in the 80s Kunen showed that absoluteness to ccc forcing extensions is equiconsistent with a weakly compact cardinal. More recently, Schindler showed that absoluteness to proper forcing extensions is equiconsistent with a remarkable cardinal. (Remarkable cardinals will be defined in the talk.) Schindler’s proof does not resemble Kunen’s, however, using almost-disjoint coding instead of Kunen’s innovative method of coding along branchless trees. We show how to reconcile these two proofs, giving a new proof of Schindler’s theorem that generalizes Kunen’s methods and suggests further investigation of non-thin trees.

## David J. Fernández Bretón: Models of set theory with union ultrafilters and small covering of meagre

Thursday, February 15, 2018, from 4 to 5:30pm
East Hall, room 3088

Speaker: David J. Fernández Bretón (University of Michigan)

Title: Models of set theory with union ultrafilters and small covering of meagre

Abstract:

Union ultrafilters are ultrafilters that arise naturally from Hindman’s finite unions theorem, in much the same way that selective ultrafilters arise from Ramsey’s theorem, and they are very important objects from the perspective of algebra in the Cech–Stone compactification. The existence of union ultrafilters is known to be independent from the ZFC axioms (due to Hindman and Blass–Hindman), and is known to follow from a number of set-theoretic hypothesis, of which the weakest one is that the covering of meagre equals the continuum (this is due to Eisworth). I will show that such hypothesis is not a necessary condition, by exhibiting a number of different models of ZFC that have a covering of meagre strictly less than the continuum, while at the same time satisfying the existence of union ultrafilters.

## Wang Wei: Combinatorics and Probability in First and Second Order Arithmetic

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 14 February 2018, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Wang Wei

Title: Combinatorics and Probability in First and Second Order Arithmetic

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:
Recent years see emergence of connections between the reverse mathematics
of Ramsey theory and computable measure theory or algorithmic randomness.
Here we consider two simple propositions in measure theory which have
interesting connections to the reverse mathematics of Ramsey theory. The
first is that every set X in Cantor space of positive Lebesgue measure is
non-empty. If X is assumed to be effectively closed then this is the
well-known axiom WWKL-0. However, if X is allowed to be a
little wilder and the proposition is twisted a bit, then it could help in
understanding the first order theory of some Ramseyan theorems. The second
is that every set X in Cantor space of positive measure has a perfect
subset. This proposition is somehow related to a tree version of Ramsey's
theorem. But unlike the first one, it is not familiar to people either in
algorithmic randomness or reverse mathematics.