BEGIN:VCALENDAR
VERSION:2.0
PRODID:ILLC Website
BEGIN:VEVENT
UID:/NewsandEvents/Events/Upcoming-Events/newsitem
/6870/8-May-2015-Cool-Logic-Ugur-Dogan-Humboldt-Un
iversity-of-Berlin-
DTSTAMP:20150430T000000
SUMMARY:Cool Logic, Ugur Dogan (Humboldt Universit
y of Berlin)
ATTENDEE;ROLE=Speaker:Ugur Dogan (Humboldt Univers
ity of Berlin)
DTSTART:20150508T173000
DTEND:20150508T183000
LOCATION:ILLC Seminar Room (F1.15), Science Park 1
07, Amsterdam
DESCRIPTION:In this talk, we will construct the se
t of Hyperreal Numbers using the help of Model The
ory. The set of Hyperreal Numbers is a field conta
ining real numbers with the addition of "infinitel
y small" and "infinitely big" numbers. We will be
gin with some historical background of Newton's (a
nd Leibniz's, as well) work (differentiation) and
why he needed the concept of "infinitely small" nu
mbers. Then to construct the set of Hyperreal Numb
ers, we will introduce some Model Theoretic concep
ts (such as languages, structures, sentences and e
lementarily equivalence) and Los's Theorem. Then,
we will construct the nonstandard extension of the
set of real numbers which we will call "the set o
f Hyperreal Numbers" and we will proceed with exam
ples of some actual hyperreal numbers and the exte
nsions of some classical functions from standard a
nalysis, such as exponential function and trigonom
etric functions. If time permits, we will see some
basic theorems in Nonstandard Analysis, such as R
obinson's Compactness Criterion. For more informa
tion, see http://www.illc.uva.nl/coollogic/ or con
tact coollogic.uva at gmail.com
X-ALT-DESC;FMTTYPE=text/html:\n In this
talk, we will construct the set of Hyperreal Numbe
rs using the help of Model Theory. The set of Hype
rreal Numbers is a field containing real numbers w
ith the addition of "infinitely small" a
nd "infinitely big" numbers.

\n
We will begin with some historical background
of Newton's (and Leibniz's, as well) work (differ
entiation) and why he needed the concept of "
infinitely small" numbers. Then to construct
the set of Hyperreal Numbers, we will introduce so
me Model Theoretic concepts (such as languages, st
ructures, sentences and elementarily equivalence)
and Los's Theorem. Then, we will construct the non
standard extension of the set of real numbers whic
h we will call "the set of Hyperreal Numbers&
quot; and we will proceed with examples of some ac
tual hyperreal numbers and the extensions of some
classical functions from standard analysis, such a
s exponential function and trigonometric functions
. If time permits, we will see some basic theorems
in Nonstandard Analysis, such as Robinson's Compa
ctness Criterion.

\n \n For more i
nformation, see http://www.illc.uva.nl/c
oollogic/ or contact coollogi
c.uva at gmail.com

\n
URL:/NewsandEvents/Events/Upcoming-Events/newsitem
/6870/8-May-2015-Cool-Logic-Ugur-Dogan-Humboldt-Un
iversity-of-Berlin-
END:VEVENT
END:VCALENDAR