This Week in Logic at CUNY:

– – – – Monday, Apr 25, 2011 – – – –

– – – – Tuesday, Apr 26, 2011 – – – –

Mini-conference in Logic and Games

Tuesday, April 26, The Graduate Center of CUNY, Room 5417

9:30 AM – 10 AM, coffee in the Mathematics Lounge, room 4214

All talks in Room 5417

10 AM: Zhaoqing Xu (Peking University, China)

Capturing Lewis’s “Elusive Knowledge”

Abstract. David Lewis developed the most prominent version of epistemic contextualism in [Lewis, 1996]. In this work, I propose a formalization of his account by representing Lewis’s uneliminated relevant possibilities as the intersection of two accessible relations. Trivial as it may seem, such formalization avoids both the problem of evaluating epistemic formulas at irrelevant possibilities [Holliday, 2010] and the factivity problem [Rebuschi & Lihoreau, 2008]. Moreover, my formalization answers partly to Holliday’s question how a relevant alternatives theorist should handle

higher-order knowledge and allows a more subtle interaction with belief.

10:45 AM: Hsing-chien Tsai (National Chung-Cheng University, Taiwan) “Elementary Mereological Theories”

Abstract. The formal language of mereology has only one non-logical symbol, a binary predicate P, which stands for “being a part of”. Most philosophers believe that P must at least define a partial ordering, that is, it is reflexive, anti-symmetric and transitive. Thus the following three basic axioms will be posited and the theory

axiomatized by them is called Ground Mereology (GM), which is exactly the theory of partial orderings. (P1) xPxx (P2) xy((PxyPyx)x=y) (P3) xyz((PxyPyz)Pxz). Let’s define three additional predicates as follows. Proper Part: PPxy =df Pxyxy Overlap: Oxy =df z(PzxPzy) Underlap: Uxy =df z(PxzPyz) The following is a list of other mereological axioms or axiom schema which can be found in the literature, and a mereological theory is normally formed by adding some of them on top of GM. (EP: extensionality)

xy(zPPzx(z(PPzxPPzy)x=y)) (WSP: weak supplementation) xy(PPxyz(PPzyOzx)) (SSP: strong supplementation)

xy(Pyxz(PzyOzx)) (FS: finite sum) xy(Uxyzw(Owz(OwxOwy))) (FP: finite product) xy(Oxyzw(Pwz(PwxPwy))) (C:

complementation) x(zPzxzw(PwzOwx)) (G: existence of the greatest member) xyPyx (A: atomicity) xy(PyxzPPzy), where y is an “atom”, for it has no proper part. (F: fusion)

xzy(Oyzx(Oyx)), for any formula where z and y do not occur free. It turns out that any theory which can be formed by using the foregoing axioms or axiom schema is in a sense a subtheory of the elementary theory of Boolean algebras (ETB) or of the theory of infinite atomic Boolean algebras (IAB). It is known that GM is undecidable while ETB and IAB are decidable. It is then interesting to look into the behaviors in terms of decidability of those mereological theories located in between. I will give a complete picture on the decidability of those mereological theories which can be formed by using the axioms or axiom schema listed above, and all kinds of undecidability, such as inseparability, finitely inseparability, essential undecidability, strong undecidability and hereditary undecidability, will be considered.

11:30 AM – 11:45 AM, break

11:45 AM: Floor Sietsma (Centrum Wiskunde & Informatica, Netherlands), “Logics for Modeling Communication with Messages”

Abstract. When agents communicate their knowledge changes and we want to model this in a logical way. Current approaches look either only at the knowledge without considering explicit messages, or look mainly at messages without having a clear focus on the knowledge of the agents. We want to combine these two viewpoints by proposing a new logic that models both explicit messages and agent’s knowledge. We present two distinct approaches that look at the problem from a different angle and make different assumptions we about the agents.

– – – – Wednesday, Apr 27, 2011 – – – –

Models of Peano Arithmetic

Wednesday, April 27, 2011 4:00 pm Math Thesis Room, GC 4214-03 Professor Ermek Nurkhaidarov (Penn State Mont Alto)

On interstices in models of Arithmetic

Abstract. In this talk we will investigate properties of interstices in countable arithmetically saturated models of Peano Arithmetic. In particular we will discuss moving interstitial gaps lemma and existence of elements whose stabilizers are maximal.

– – – – Thursday, Apr 28, 2011 – – – –

– – – – Friday, Apr 29, 2011 – – – –

Model Theory Seminar

Friday, April 29, 2011 12:30 pm GC 6417

Professor Roman Kossak (The City University of New York)

Elementary pairs of models of Peano Arithmetic

Abstract. There is a great variety of isomorphism types of pairs (N,M) of models of PA, where M is an elementary submodel of N. The objective is to see to what extent the complexity (N,M) is expressed by Th(N,M). I will present some interesting examples.

Logic Workshop

Friday, April 29, 2011 2:00 pm GC 6417

Professor Deirdre Haskell (McMaster University)

Some model theory of valued fields

Abstract. Valued fields have long been known to be amenable to model- theoretic analysis. I will review the classical quantifier elimination results, and discuss the more recent elimination of imaginaries results. Then I will consider the enriched structure of a valued field in a language with function symbols to be interpreted on the field by restricted analytic functions, and the associated QE and EI results. No knowledge of valued fields will be assumed.

Logic and Games Seminar

Friday, April 29, 2011 4:15 pm GC, Room 4419

Dr. Zach Weber (University of Melbourne)

Paraconsistent Mathematics

Abstract. There are logical paradoxes. Plausibly, these put pressure on classical logic. But any call for logic revision is beholden to mathematics. No math? No revision. I will consider a paraconsisent logic and set theory, and, through several examples from real analysis, show that it fares well as a way to do mathematics.

Next Week in Logic at CUNY:

– – – – Monday, May 2, 2011 – – – –

– – – – Tuesday, May 3, 2011 – – – –

– – – – Wednesday, May 4, 2011 – – – –

– – – – Thursday, May 5, 2011 – – – –

– – – – Friday, May 6, 2011 – – – –

Model Theory Seminar

Friday, May 6, 2011 12:30 pm GC 6417

Speaker TBA

More model theory of modules

Logic Workshop

Friday, May 6, 2011 2:00 pm GC 6417

Professor Alexey Ovchinnikov (City University of New York, Queens College) Bounds for orders of derivatives in differential elimination algorithms

Abstract. Differential elimination algorithms simplify systems of polynomial ordinary and partial differential equations. We will discuss how one can bound the number of differentiations these algorithms make and the orders of derivatives in the output. The goal is to further understand the computational complexity of such algorithms.

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