This Week in Logic at CUNY

 

Set Theory Seminar
Friday, November 9, 2012, 10:00am GC 6417
Shoshana Friedman
Extending a property of HOD-supercompactness. Or Not.

Abstract: I will discuss a result of Sargsyan and his method of proof
in order to show why a theorem from my dissertation was incorrect, and
some of the interesting results we discovered in an effort to save the
theorem.

Model Theory Seminar
Friday, November 9, 2012, 12:30pm-1:45pm, GC 6417
Hunter Johnson (John Jay College)

Logic Workshop
Friday, November 9, 2012 2:00 pm GC 6417
Prof. Philip Ehrlich (Ohio University)
The surreal number tree

In his monograph On Numbers and Games [1], J. H. Conway introduced a
real-closed
field containing the reals and the ordinals as well as a great many
less familiar numbers including omega, omega/2, 1/omega, \sqrt{omega}
and omega-pi to name only a few, where omega is the least infinite
ordinal. This particular real-closed field, which Conway calls No, is
so remarkably inclusive that, subject to the proviso that
numbers—construed here as members of ordered “number” fields—be
individually definable in terms of sets of NBG, it may be said to
contain “All Numbers Great and Small.” In addition to its inclusive
structure as an ordered field No has a rich algebraico-binary
tree-theoretic structure, or simplicity hierarchy, that emerges from
the recursive clauses in terms of which it is defined.

Among the striking simplicity-hierarchical features of No is that
every surreal number
can be assigned a canonical “proper name”—called its Conway name (or
normal form)—that is a reflection of its characteristic
simplicity-hierarchical properties.

In [2], answers are provided for the following two questions that are
motivated by No’s
structure as an ordered binary tree:
(i) Given the Conway name of a surreal number, what are the Conway
names of its two
immediate successors?
(ii) Given a chain of surreal numbers of infinite limit length, what
is the Conway name of the
immediate successor of the chain?
The purpose of this talk is to provide an introduction to [2].

[1] J. H. Conway, On numbers and games, Academic Press, 1976.
[2] P. Ehrlich, Conway Names, the Simplicity Hierarchy and the
Surreal Number Tree, The
Journal of Logic and Analysis 3 (2011), pp. 1-26.

Seminar in Logic and Games
Friday, November 9, 2012, 4:15 PM, room 4419, CUNY Graduate Center
Paraconsistent Dynamics
Koji Tanaka (University of Auckland, New Zealand)

Can we define dynamic operations studied in the framework of dynamic
epistemic logic using paraconsistent logic? This question has not been
addressed in the literature (as far as we know). In this paper, we
study two dynamic operations: public announcement and belief change.
We will show that we can consider two kinds of public announcement and
belief change: aletheic and classical. We will demonstrate that
aletheic operations can be defined using a paraconsistent logic
(though not relevant) and that classical operations cannot be defined
paraconsistently.

Special Event
Time: Friday November 9, 5:00 PM
Place: Philosophy Hall room 716 (on the seventh floor)
Speaker: Dana S. Scott (University Professor Emeritus, Carnegie Mellon University, and Visiting Scholar, University of California, Berkeley)
Title: Lambda Calculus: Then and Now

Abstract: A very fast development in the early 1930’s following
Hilbert’s codification of Mathematical Logic led to the
Incompleteness Theorems, Computable Functions, Undecidability
Theorems, and the general formulation of Recursive Function
Theory. The so-called Lambda Calculus played a key role. The
history of these developments will be traced, and the much later
place of Lambda Calculus in Mathematics and Programming-
Language Theory will be outlined.

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