*Models of Peano Arithmetic*

Monday, March 19, 2012 7:00 pm Room 4214-03

Professor David Marker (University of Illinois at Chicago)

The Mourgues Rassayre Theorem

*Set Theory Seminar*

Friday, March 23, 2012 10:00 am GC 6417

Professor Gunter Fuchs (The City University of New York)

Contructing a Souslin almost Kurepa tree

Abstract. In joint work with Joel Hamkins, we investigated various

strengthenings of rigidity of a Souslin tree. Many of these notions

come from viewing the Souslin tree T as a notion of forcing. For

example, T is absolutely rigid of T is rigid after forcing with T. A

quite intriguing strong form of rigidity is the unique branch

property, which says that forcing with T adds precisely one branch to

T. In our collaborative work, we were able to establish a complete

diagram of implications and non-implications between these and various

other forms of rigidity. One question that arose was how badly a rigid

Souslin tree can violate the unique branch property. In this talk, I

am going to sketch the construction of a rigid Souslin tree T that is

almost Kurepa, which means that after forcing with T, T becomes a

Kurepa tree – so it violates the unique branch property as badly as

thinkable.

*Model Theory Seminar*

Friday, March 23, 2012 12:30 pm GC 6417

Professor Jouko Väänänen (University of Helsinki and University of Amsterdam)

On second-order model theory III

Abstract. This mini course will cover the following topics: second

order characterizable structures, Henkin models, Completeness Theorem,

internal categoricity, and existence of second order equivalent

non-isomorphic models.

*Logic Workshop*

Friday, March 23, 2012 2:00 pm GC 6417

Professor Curtis Franks (Department of Philosophy, University of Notre Dame)

Gödel’s last thought on Gentzen’s consistency proof

Abstract. A transcript of a series of conversations between Kurt Gödel

and Sue Toledo from the years 1972 to 1975 was recently made available

and published in Kennedy and Kossak 2011. Among the most striking

remarks recorded in these notes is Gödel’s claim that Hilbert’s

program “was completely refuted,” though by Gerhard Gentzen’s work

and not by Gödel’s own results. This is exactly opposite the customary

appraisal of these matters. Drawing from the details of Gödel’s late

thought and some basic technical observations, we can understand how

Gödel could make such a claim and begin to appreciate an attitude

towards foundations that differs greatly from familiar ideas.

Next Week in Logic at CUNY:

– – – – Monday, Mar 26, 2012 – – – –

Models of Peano Arithmetic

Monday, March 26, 2012 7:00 pm Room 4214-03

Professor Alfred Dolich (Kingsborough Community College)

Omega-1 like models of Presburger arithmetic

– – – – Tuesday, Mar 27, 2012 – – – –

– – – – Wednesday, Mar 28, 2012 – – – –

– – – – Thursday, Mar 29, 2012 – – – –

– – – – Friday, Mar 30, 2012 – – – –

Model Theory Seminar

Friday, March 30, 2012 12:30 pm GC 6417

Mr. Manuel Alves (Ph.D. Program in Mathematics, Graduate Center of CUNY)

Introduction to elementary duality for modules

– – – – Other Logic News – – – –

– – – – Web Site – – – –

The majority of this information, including an interactive calendar of

future events, can be found at our website:

http://nylogic.org/Calendar