This Week in Logic at CUNY

Computational Logic Seminar
Tuesday, October 1, 2013 2:00 pm Graduate Center, rm. 3209
Speaker: Antonis Achilleos Graduate Center CUNY
Title: On the Complexity of Multi-agent Justification Logic Under Interacting Justifications

We introduce a family of multi-agent justification logics with interactions between the agents’ justifications, by extending and generalizing the two-agent versions of LP introduced by Yavorskaya in 2008. Known concepts and tools from the single-agent justification setting are adjusted for this multiple agent case. We present tableau rules and some preliminary complexity results: in several important cases, the satisfiability problem for these logics remains in the second level of the polynomial hierarchy, while for others it is PSPACE or EXP-hard.

Models of PA
Wednesday, October 2, 2013 6:30 pm GC 4214.03
Speaker: Roman Kossak The City University of New York
Title: Fullness

A model $M$ of PA is full if for every definable in $(M,omega)$ set $X$, $Xcap omega$ is coded in $M$. In a recent paper, Richard Kaye proved that $M$ is full if and only if its standard system is a model of full second order comprehension. Later in the semester we will examine Kaye’s proof. In this talk I will discuss some preliminary results and I will show an example of a model that is not full, using an argument that does not depend on Kaye’s theorem

Set theory seminar
Friday, October 4, 2013 10:00 am GC 6417
Speaker: Victoria Gitman The New York City College of Technology (CityTech), CUNY
Title: Embeddings among $\omega_1$-like models of set theory

An $omega_1$-like model of set theory is an uncountable model, all of whose initial segments are countable. The speaker will present two $omega_1$-like models of set theory, constructed using $Diamond$, which are incomparable with respect to embeddability: neither is isomorphic to a submodel of the other. Under a suitable large cardinal assumption, there are such models that are well-founded.

Model theory seminar
Friday, October 4, 2013 12:30 pm GC6417
Speaker: David Marker University of Illinois at Chicago
Title: Real closures of $\omega_1$-like models of PA
In an earlier seminar I showed that assuming diamond we can build many $omega_1$-like models of PA with the same standard system but non-isomorphic real closures. In this lecture I will show how to do this without diamond. This is joint work with Jim Schmerl and Charlie Steinhorn.