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.
Wednesday, October 2, 2013 6:30 pm GC 4214.03
Speaker: Roman Kossak The City University of New York
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
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.
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.
CUNY Logic Workshop
Friday, October 4, 2013 2:00 pm GC 6417
Speaker: Hans Schoutens The City University of New York
Title: Why model-theorists shouldn’t think that ACF is easy
We all learned that stability theory derived many of its ideas from what happens in ACF, where everything is nice and easy. After all ACF has quantifier elimination and is strongly minimal, decidable, superstable, uncountably categorical, etc. However, my own struggles with ACF have humbled my opinion about it: it is an awfully rich theory that encodes way more than our current knowledge. I will discuss some examples showing how “difficult” ACF is: Grothendieck ring, isomorphism problem, set-theoretic intersection problem. Oddly enough, RCF seems to not have any of these problems. It is perhaps my ignorance, but I have come to think of RCF as much easier. Well, all, of course, is a matter of taste.