# This Week in Logic at CUNY

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.
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

– – – – Web Site – – – –

The majority of this information, including an interactive calendar of
future events, can be found at our website:

http://nylogic.org/Calendar