This Week in Logic at CUNY:

– – – – Monday, Apr 2, 2012 – – – –

Models of Peano Arithmetic

Monday, April 2, 2012 7:00 pm Room 4214-03

Dr. Kerry Ojakian (Department of Mathematics, St. Joseph College)

Integer parts of real closed fields and weaker fragments of arithmetic

– – – – Tuesday, Apr 3, 2012 – – – –

Computational Logic Seminar

Time 2:00 – 4:00 PM, April 3, 2012, Room 3209.

Speaker: Sergei Artemov (Graduate Center)

Title: The Logic of Proofs is sometimes smarter than BHK semantics.

Abstract: The Logic of Proofs, combined with Goedel’s embedding of

intuitionistic logic into modal logic, provides a sound formalization

of the Brouwer-Heyting-Kolmogorov (BHK) semantics. In this talk, we

will discuss BHK clauses in which provability semantics straightens up

apparent leaks in the original BHK.

1. The universal quantifier clause in the original BHK [a

constructive proof of ‘for all x F(x)’ is an algorithm that for each c

returns a proof of F(c)] appears to be flawed since it certifies

trivial “constructive proofs” for each true Pi-1 sentence. Goedel’s

translation refines this clause to “a constructive proof of `for all x

F(x)’ is a pair (p,d) where p is a function and d is a classical proof

that, for each c, p(c) is a proof of F(c)” thus closing this

well-known leak in the BHK semantics.

2. The BHK clause of negation is reduced to implication: `not F’ is

read as `F -> \bot’ where \bot is a constant sentence that has no

proofs. If taken literally, this yields that each non-provable

sentence F is constructively false. Goedel translation and the Logic

of Proofs fix this leak too. For true insight in BHK semantics of

independent sentences one needs to use a quite technical machinery of

joint logics of explicit proofs and provability LPP/GLA developed

earlier by the speaker, Tanya Yavorskaya, Elena Nogina, and Hide

Kurokawa.

– – – – Wednesday, Apr 04, 2012 – – – –

Model Theory Seminar

Wednesday, April 4, 2012 6:30 pm Room 4012-03

Professor Alexander Bernstein (Universidad de los Andes)

Ample metric generics (joint work with Itaï Ben Yaacov and Julien Melleray)

Abstract. . We recall the notion of ample generics introduced by

Kechris and Rosendal and how it is related to Fraïssé constructions.

We define and study the notion of ample metric generics for a Polish

topological group, which is a weakening of the notion of ample

generics. Examples of Polish groups with ample metric generics include

the unitary group of a separable Hilbert space, and the automorphism

group of the Lebesgue measure algebra on [0,1]. As an application, we

deduce from this and earlier work of Kittrell and Tsankov that this

last group has the automatic continuity property, i.e., any morphism

from automorphism group of the Lebesgue measure algebra into a

separable topological group is continuous.

– – – – Thursday, Apr 05, 2012 – – – –

– – – – Friday, Apr 06, 2012 – – – –

** CUNY Spring Break April 6 – 15 **

Next Week in Logic at CUNY:

** CUNY Spring Break April 6 – 15 **

– – – – Other Logic News – – – –

Second Call for Papers

Logic Workshop at Buenos Aires – A Tribute to Horacio Arló-Costa

SADAF, the Argentine Society for Philosophical Analysis, is

organizing a Tribute to Horacio Arló-Costa, to take place in Buenos

Aires, August 2nd to 4th, 2012.

* Deadline for reception of submissions: April 30th, 2012

For further particulars, please check SADAF website at

www.sadaf.org.ar or contact us by sending an e-mail to

info@sadaf.org.ar

– – – – Web Site – – – –

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future events, can be found at our website:

http://nylogic.org/Calendar

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