**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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