*Models of Peano Arithmetic*

Monday, March 12, 2012 7:00 pm Room 4214-03

Professor Alfred Dolich (Kingsborough Community College)

The D’Auquino Knight Starchenko Theorem

*Computational Logic Seminar*

Time 2:00 – 4:00 PM, March 13, Room 3209.

Speaker: Yuri Gurevich, Microsoft Research

Title: Distributed Knowledge Authorization Language (DKAL): Managing

Policies and Trust

Abstract: With the advent of cloud computing, the necessity arises to

manage policies and trust automatically and efficiently. In a

brick-and-mortar (B&M) setting, clerks learn unwritten policies from

trustworthy peers. And if they don’t know a policy, they know whom to

ask. In the B&M-to-cloud transition, the clerks disappear. Policies

have to be explicit and managed automatically. The more challenging

problem yet is how to handle the interaction of the policies of

distrustful principals, especially in federated scenarios where there

is no central authority. The DKAL project was created to deal with

such problems. The new language, new logics and tools keep evolving.

We discuss the current state of the project.

*Other New York Logic Events + Set Theory Seminar*

Friday, March 16, 2012 12:00 pm TBA

Mr. Brent Cody (The Graduate Center of The City University of New York)

Some results on large cardinals and the continuum function

Abstract. The speaker will defend his dissertation.

*Model Theory Seminar*

Friday, March 16, 2012 12:30 pm GC 6417

Mr. Whanki Lee (CUNY Graduate Center)

Chronically resplendent models and totally resplendent models.

*Logic Workshop*

Friday, March 16, 2012 2:00 pm GC 6417

Professor Julia Knight (University of Notre Dame)

Integer parts for real closed exponential fields

Abstract. A real closed field is a model R of Th(ℜ). An integer part

for a real closed field R is a discrete ordered subring I such that

for all r in R, there exists i in I with i ≤ r < i+1. A real closed

exponential field is a model of a certain computably axiomatizable

fragment of Th(ℜ,2x). An exponential integer part is an integer part I

such that for positive i in I, 2i is in I. Mourgues and Ressayre

showed that every real closed field has an integer part. Ressayre

showed that every real closed exponential field R has an exponential

integer part. Ressayre’s construction is canonical once we fix a well

ordering of R and a residue field section (i.e., a maximal Archimedean

subfield). Each step of the construction seems effective. Even so,

there is an arithmetical real closed exponential field R, with an

arithmetical residue field section k and an arithmetical ordering < of

type ω+ω (R is low, and k and < are Δ30), such that Ressayre’s

construction of an exponential integer part is not completed in the

least admissible set.

This is joint work among Paola D’Aquino, Karen Lange, Salma Kuhlmann,

and the speaker.

– – – – Monday, Mar 19, 2012 – – – –

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

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.