This Week in Logic at CUNY

This Week in Logic at CUNY:

 

Special Event
Staged reading of Daniel Kehlmann’s play “Ghosts in Princeton” about
the life of Kurt Gödel.
Location: Center for Jewish History, Forchheimer Auditorium, 151 W
16th St in Manhattan, 212-744-6400
Tuesday, May 1st, 6pm, tickets are $10.
For more information: http://www.goethe.de/ins/us/ney/ver/en9162510v.htm
(NOTE: This event is not associated with CUNY)

 

 

Set Theory Seminar
Friday, May 4, 2012 10:00 am GC 6417
Professor Victoria Gitman (NYC College of Technology (CUNY))
Models of ZFC minus powerset that are not definable in their set
forcing extensions

Abstract. It took four decades since the invention of forcing for set
theorists and to ask (and answer) what post factum seems as one of the
most natural questions regarding forcing. Is the ground model a
definable class of its set forcing extensions? Using techniques
developed by Hamkins, Laver showed that the answer is, indeed, yes.
The result is also due independently to Woodin. The requirement that P
is a set forcing is a necessary one, since the ground model need not
be definable in a class forcing extension. Since, in many contexts,
set theorists force over models of ZFC-, the theory ZFC without the
powerset axiom, it is natural to inquire whether Laver’s theorem holds
in this case as well. The answer turns out to be no. Indeed, using
different preparatory forcing, one can create numerous counterexamples
of the form H_\kappa^+. The downside of the counterexample models is
that the powerset of the forcing notion in whose extension they are
not definable is a proper class in the model, making the situation
much too similar to class forcing to be truly satisfying.
Surprisingly, the only known counterexample in which the powerset of
the forcing notion is an element of the model needs an I_0 cardinal,
one of the strongest large cardinal notions not known to be
inconsistent. In this talk, I will discuss these counterexamples and
the associated open questions.

Model Theory Seminar
Friday, May 4, 2012 12:30 pm GC 6417
Professor David Marker (University of Illinois at Chicago)
Definability of types in o-minimal theories revisited

Abstract. I will discuss a new proof, due to Eric Walsberg of the
definability of types theorem for o-minimal theories.

Friday, May 4, 2012 2:00 pm GC 6417
Professor Arthur W. Apter (Baruch College of CUNY)
Some remarks on j : V → V

Abstract. I will discuss some consequences of the existence of a
nontrivial elementary embedding of the universe into itself. To avoid
Kunen’s famous result that no such embedding can exist if the Axiom of
Choice is true, the context will be one in which the Axiom of Choice
is false. I will speak about old joint work with Grigor Sargsyan and
more recent joint work (still in progress) with Brent Cody.

Next Week in Logic at CUNY:

– – – – Monday, May 7, 2012 – – – –

– – – – Tuesday, May 8, 2012 – – – –

– – – – Wednesday, May 9, 2012 – – – –

Models of Peano Arithmetic
Wednesday, May 9, 2012 6:30 pm Room 4214-03
Professor Leszek Kolodziejczyk (Institute of Mathematics, University
of Warsaw)
Open Induction-style methods in the study of fragments of bounded arithmetic

Abstract. Sam Buss’ bounded arithmetic S_2, defined in the mid-80’s,
has been studied mostly because of its connections with computational
complexity and propositional proof complexity. The main goal in the
area, to separate natural fragments of S_2 from the full theory, is
apparently out of reach except for some very weak fragments. For this
reason, attention has largely shifted to somewhat different questions,
but a better understanding of the border between “very weak”
subtheories of S_2 and those “too strong for current methods” is
still desirable. In this talk, I will discuss some separations
obtained by techniques inspired by open induction, first introduced
into bounded arithmetic by Boughattas and Ressayre.

– – – – Thursday, May 10, 2012 – – – –

– – – – Friday, May 11, 2012 – – – –

Model Theory Seminar
Friday, May 11, 2012 12:30 pm GC 6417
Professor Philipp Rothmaler (The City University of New York, BCC)
More examples: definable subgroups of modules and Ziegler spectra of rings

Abstract. This talk is first of all intended as illustration to the
previous talk on modules in that I will present more examples of pp
definable subgroups and more pictures. I will then introduce the
Ziegler spectrum of a ring, a central concept of the model theory of
modules, and compute it for the integers. Some other examples of
Ziegler spectra will be mentioned as well.

Friday, May 11, 2012 2:00 pm GC 6417
Professor Philipp Rothmaler (The City University of New York, BCC)
Mittag-Leffler modules

– – – – Other Logic News – – – –

Staged reading of Daniel Kehlmann’s play “Ghosts in Princeton” about
the life of Kurt Gödel.
Location: Center for Jewish History, Forchheimer Auditorium, 151 W
16th St in Manhattan, 212-744-6400
Tuesday, May 1st, 6pm, tickets are $10.
For more information: http://www.goethe.de/ins/us/ney/ver/en9162510v.htm

– – – – Web Site – – – –

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

http://nylogic.org/Calendar

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