Welcome to New York Logic!

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## Upcoming talks and events:

# Harrington’s Principle and remarkable cardinals

It is open whether $\Pi^1_1$ determinacy implies the existence of $0^{\#}$ in 3rd order arithmetic, call it $Z_3$. We compute the large cardinal strength of $Z_3$ plus “there is a real $x$ such that every $x$-admissible is an $L$-cardinal.” This is joint work with Yong Cheng.

# NEXP-completeness and Universal Hardness Results for Justification Logic

We provide a lower complexity bound for the satisfiability problem of a multi-agent justification logic, establishing that there are certain NEXP-complete multi-agent justification logics with interactions. We then use a simple modification of the corresponding reduction to prove that satisfiability for all multi-agent justification logics in a general class we consider is $Sigma_2^p$-hard — given certain reasonable conditions. Our methods improve on these required conditions for the same lower bound for the single-agent justification logics, proven by Buss and Kuznets in 2009, thus answering one of their open questions.

Link to paper on arXiv:

http://arxiv.org/abs/1503.00362

# The undecidability of lattice-ordered groups II

In this talk I will discuss conjugacy in the automorphism group of the rationals as a linearly ordered set, and then show that the integers, together with addition and multiplication, can be interpreted in Aut(Q), and thus that the theory of Aut(Q) is undecidable.

Friday, April 10, 2015

# Spring break

CUNY’s spring vacation is April 3-11, 2015. Therefore, no seminars will meet at the Graduate Center on April 3, nor on April 10.