BEGIN:VCALENDAR
PRODID:-//PSU Mathematics Department//Seminar iCalendar Generator//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Logic Seminar
X-WR-TIMEZONE:America/New_York
BEGIN:VTIMEZONE
TZID:America/New_York
X-LIC-LOCATION:America/New_York
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:19700308T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:19701101T020000
RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150825T143000
DTEND;TZID=America/New_York:20150825T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27011
SUMMARY:Logic Seminar - Organizational Meeting
DESCRIPTION:Seminar: Logic Seminar\nTitle: Organizational Meeting\nAbstract
: This is an organizational meeting to plan the seminar for the semester.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150901T143000
DTEND;TZID=America/New_York:20150901T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27015
SUMMARY:Logic Seminar - Degrees of unsolvability. Part 1: introduction
DESCRIPTION:Seminar: Logic Seminar\nTitle: Degrees of unsolvability. Part
1: introduction\nSpeaker: Stephen G. Simpson\, Penn State\nAbstract: This
series of talks is based on my recent 3-hour tutorial at the Computability
in Europe conference in Bucharest. An important 20th century discovery i
s that there are algorithmically unsolvable problems in virtually every br
anch of mathematics. Degrees of unsolvability are an attempt to measure t
he "amount" or "extent" of the unsolvability of such problems. They are b
ased on the idea of "reducibility" of one problem to another. In this int
roductory talk we define and discuss two particular degree structures: the
Turing degrees\, and the Muchnik degrees. We point out that the Muchnik
degrees are the completion of the Turing degrees\, similarly to how the re
al numbers are the completion of the rational numbers. We discuss specifi
c examples of Turing degrees\, and we give at least one specific example o
f a Muchnik degree which is not a Turing degree. (There are many more suc
h examples\, and we shall discuss some of them in later talks in this seri
es.) We point out how the Muchnik degrees provide a rigorous implementati
on of Kolmogorov's calculus of problems.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150908T143000
DTEND;TZID=America/New_York:20150908T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27019
SUMMARY:Logic Seminar - No seminar this week
DESCRIPTION:Seminar: Logic Seminar\nTitle: No seminar this week
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150915T143000
DTEND;TZID=America/New_York:20150915T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27023
SUMMARY:Logic Seminar - Degrees of unsolvability. Part 2: examples
DESCRIPTION:Seminar: Logic Seminar\nTitle: Degrees of unsolvability. Part
2: examples\nSpeaker: Stephen G. Simpson\, Penn State\nAbstract: This seri
es of talks is based on my recent 3-hour tutorial at the Computability in
Europe conference in Bucharest. An important 20th century discovery is tha
t there are algorithmically unsolvable problems in virtually every branch
of mathematics. Degrees of unsolvability are an attempt to measure the "am
ount" or "extent" of the unsolvability of such problems. They are based on
the idea of "reducibility" of one problem to another. We focus on two par
ticular degree structures: (1) the Turing degrees\, and (2) the lattice-th
eoretic completion of the Turing degrees\, also known as the Muchnik degre
es. In this talk I survey the known specific\, natural examples of Turing
degrees\, and I exhibit many specific\, natural examples of Muchnik degree
s which are not Turing degrees. I also point out how the Muchnik degrees p
rovide a rigorous implementation of Kolmogorov's nonrigorous 1932 calculus
of problems.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150922T143000
DTEND;TZID=America/New_York:20150922T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27027
SUMMARY:Logic Seminar - An Introduction to Fine Structure Theory
DESCRIPTION:Seminar: Logic Seminar\nTitle: An Introduction to Fine Structur
e Theory\nSpeaker: Jan Reimann\, Penn State\nAbstract: In his proof of the
(relative) consistency of the Continuum Hypothesis (CH)\, Gödel defined
the constructible universe L\, in which the introduction of new sets happe
ns at a "tamer" rate\, compared to the Von-Neumann universe. \n\nIn 1972\,
introduced a sophisticated technical apparatus\, fine structure theory\,
to study in detail the way new sets are defined in L. Fine structure has b
ecome one of the central components of modern set theory\, particularly th
e inner model program\, which seeks to find L-like models for large cardin
als.\n\nIt is also closely related to computability theory\, as Jensen's n
otion of projectum behaves in many ways like a Turing jump. \n\nIn a serie
s of talks\, I will give an introduction to fine structure theory\, starti
ng with a brief review of Gödel's fundamental ideas\, as well as Boolos'
and Putnam's predecessor to fine structure. In later talks\, I will cover
Jensen's J-hierarchy\, projecta and master codes\, and an application to a
lgorithmic randomness due to Reimann and Slaman.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150929T143000
DTEND;TZID=America/New_York:20150929T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27031
SUMMARY:Logic Seminar - Gambling against some Odds
DESCRIPTION:Seminar: Logic Seminar\nTitle: Gambling against some Odds\nSpea
ker: Jake Pardo\, Penn State\nAbstract: In their paper How to Gamble Again
st All Odds\, Bavly and Peretz discuss opposing betting strategies and com
pare their relative strengths. In particular\, we have two gambler each b
etting with different sets\, A and B: when is it possible for the gambler
with set A to make infinite money in the long-term while the gambler with
set B does not? What if there are infinitely many gamblers with set B tha
t all have to be kept from making infinite money? I will discuss some of
the results of Bavly and Peretz\, as well as present some open problems on
the topic. This is the first in a two part talk series.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151006T143000
DTEND;TZID=America/New_York:20151006T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27036
SUMMARY:Logic Seminar - Gambling Against Some Other Odds
DESCRIPTION:Seminar: Logic Seminar\nTitle: Gambling Against Some Other Odds
\nSpeaker: Jake Pardo\, Penn State\nAbstract: In the results we saw last w
eek regarding the relative strengths of gambling strategies\, we saw that
the proofs relied on the fact that the strategy to beat had a least positi
ve value it could bet - using this the strategy could be beaten by forcing
its gambler to either give up betting or to go broke. However\, there is
n't much known when the strategy to beat is able to make arbitrarily small
bets. I will discuss some personal work on this topic\, as well as menti
on potential future directions for this problem.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151013T143000
DTEND;TZID=America/New_York:20151013T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27040
SUMMARY:Logic Seminar - Degrees of unsolvability. Part 3: Muchnik degrees
of effectively closed sets
DESCRIPTION:Seminar: Logic Seminar\nTitle: Degrees of unsolvability. Part
3: Muchnik degrees of effectively closed sets\nSpeaker: Stephen G. Simpson
\, Penn State\nAbstract: This series of talks is based on my recent 3-hour
tutorial at the Computability in Europe conference in Bucharest. The latt
ice of all Muchnik degrees is large and complicated\, but in this talk I d
iscuss two sublattices which are smaller and hopefully more manageable. N
amely\, let E_w and S_w be the sublattices consisting of the Muchnik degre
es of nonempty\, effectively closed sets in the Cantor space and the Baire
space respectively. I prove that E_w is an initial segment of S_w\, and
I use this fact to obtain many specific\, natural examples of degrees in E
_w. I note that there is a strong analogy between E_w and E_T\, the upper
semilattice of recursively enumerable Turing degrees. I argue that E_w i
s more interesting than E_T\, because E_T contains no specific\, natural e
xamples of degrees other than the top and bottom degrees\, 0' and 0.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151020T143000
DTEND;TZID=America/New_York:20151020T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27044
SUMMARY:Logic Seminar - An Introduction to Fine Structure Theory\, part II
DESCRIPTION:Seminar: Logic Seminar\nTitle: An Introduction to Fine Structur
e Theory\, part II\nSpeaker: Jan Reimann\, Penn State\nAbstract: We contin
ue our introduction to Fine Structure Theory with the core concepts of Jen
sen's 1972 paper: rudimentary functions and the J-hierarchy\, projecta\, s
tandard codes. The machinery is rather technical\, but I will try to carve
out the essential parts in an accessible way.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151027T143000
DTEND;TZID=America/New_York:20151027T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27048
SUMMARY:Logic Seminar - Algorithmic randomness and constructive/computable
mathematics
DESCRIPTION:Seminar: Logic Seminar\nTitle: Algorithmic randomness and const
ructive/computable mathematics\nSpeaker: Jason Rute\, Penn State\nAbstract
: I will present a short history of constructive and computable measure th
eory\, focusing on connections with algorithmic randomness. Constructive m
easure theory originated in a 1919 paper of Brouwer\, which developed\, am
ong other things\, constructive definitions of "null set"\, "measurable se
t"\, "measurable function"\, and "integrable function". Brouwer's work has
been extended\, reformed\, and rediscovered in a number of settings: Russ
ian constructive mathematics\, Bishop-style constructive mathematics\, rev
erse mathematics\, computable analysis\, categorical logic\, and algorithm
ic randomness. Moreover\, many of the fathers of algorithmic randomness---
Martin-Löf\, Demuth\, and Schnorr---were motivated by constructive concer
ns.\n\nRecently\, a number of results have appeared connecting algorithmic
randomness and analysis. In many cases\, these results can be phrased as
theorems in constructive mathematics. Conversely\, the constructive theore
ms of Bishop\, Demuth\, and others have direct consequences to algorithmic
randomness.\n\nThis raises the the question\, which I will answer. "What
randomness notion is most associated with constructive mathematics?"
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151103T143000
DTEND;TZID=America/New_York:20151103T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27052
SUMMARY:Logic Seminar - When does randomness come from somewhere?
DESCRIPTION:Seminar: Logic Seminar\nTitle: When does randomness come from s
omewhere?\nSpeaker: Jason Rute\, Penn State\nAbstract: This talk is about
algorithmic randomness. A point in a probability space (in this case the
uniform measure on Cantor space) is algorithmically random if it satisfies
all "computable probability one properties." Different notions of "compu
table probability one property" gives rise to different notions of algorit
hmic randomness. One desirable property for a randomness notion to have i
s this property\, sometimes called "no randomness from nothing": if T is a
computable measure preserving map and y is algorithmically random\, then
there is some algorithmically random x such that T(x)=y. We will discuss
for which randomness notions this property holds and for which ones it doe
s not hold. We will also discuss how under suitable conditions\, this pro
perty holds for all standard randomness notions.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151110T143000
DTEND;TZID=America/New_York:20151110T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27056
SUMMARY:Logic Seminar - Diophantine Approximation and Hausdorff Dimension
DESCRIPTION:Seminar: Logic Seminar\nTitle: Diophantine Approximation and Ha
usdorff Dimension\nSpeaker: Mingyang Li\, Penn State\nAbstract: The expone
nt of irrationality measures how well a real number can be approximated by
rational numbers. Almost every number has irrationality exponent greater
than or equal to 2. Liouville numbers are those numbers which have irratio
nality exponent infinity\, while a famous theorem due to Roth shows that a
lgebraic numbers have irrationality exponent 2. \n\nThis talk will present
a classic result due to Jarnik and Besicovitch\, who independently showed
that the Hausdorff dimension of the set of reals with irrationality expon
ent greater than or equal to a has Hausdorff dimension 2/a.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151117T143000
DTEND;TZID=America/New_York:20151117T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27060
SUMMARY:Logic Seminar - Khinchin's Theorems on Metric Diophantine Approxima
tion
DESCRIPTION:Seminar: Logic Seminar\nTitle: Khinchin's Theorems on Metric Di
ophantine Approximation\nSpeaker: Mingyang Li\, Penn State\nAbstract: This
talk continues an overview over some classical results in metric diophant
ine approximation.\nWe discuss two fundamental results due to A. Khinchin
\, one concerning the \\psi-approximability of real numbers\, the other es
tablishing almost everywhere stability of the geometric mean of partial qu
otients (Khinchin's constant).
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151124T143000
DTEND;TZID=America/New_York:20151124T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27064
SUMMARY:Logic Seminar - No Seminar This Week
DESCRIPTION:Seminar: Logic Seminar\nTitle: No Seminar This Week
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151201T143000
DTEND;TZID=America/New_York:20151201T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27068
SUMMARY:Logic Seminar - Hausdorff Dimension\, Irrationality Exponents and T
heir Effectivization
DESCRIPTION:Seminar: Logic Seminar\nTitle: Hausdorff Dimension\, Irrational
ity Exponents and Their Effectivization\nSpeaker: Jan Reimann\, Penn State
\nAbstract: We generalize the classical theorem by Jarnik and Besicovitch
on the irrationality exponents of real numbers and Hausdorff dimension. Le
t a be any real number greater than or equal to 2 and let b be any non-neg
ative real less than or equal to 2/a. We show that there is a Cantor-like
set with Hausdorff dimension equal to b such that\, with respect to its un
iform measure\, almost all real numbers have irrationality exponent equal
to a. We give an analogous result relating the irrationality exponent and
the Hausdorff dimension of individual real numbers. We prove that there is
a Cantor-like set such that\, with respect to its uniform measure\, almos
t all reals in the set have effective Hausdorff dimension equal to b and i
rrationality exponent equal to a.\n\nThis is joint work with V. Becher and
T. Slaman.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151208T143000
DTEND;TZID=America/New_York:20151208T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27072
SUMMARY:Logic Seminar - Triviality and lowness for K-reducibility and relat
ed reducibilities
DESCRIPTION:Seminar: Logic Seminar\nTitle: Triviality and lowness for K-red
ucibility and related reducibilities\nSpeaker: William C. Calhoun\, Blooms
burg University\nAbstract: A set of natural numbers A is K-trivial if K(A|
n) <= K(n)+O(1) for all natural numbers n (where A|n is A restricted to n
and K is prefix-free Kolmogorov complexity). The set A is low for K if K^
{A}(y)=K(y)+O(1) for all binary strings y. These definitions seem quite d
ifferent. K-triviality indicates that initial segments of A have the lowe
st possible complexity\, while lowness for K indicates that A is too weak
as an oracle to reduce the complexity of any string. The remarkable equiv
alence of the two definitions was shown in [2]. Replacing prefix-free co
mplexity by monotone complexity in the definition of K-trivial\, we obtain
the Km-trivial sets. Every K-trivial set is Km-trivial and all Turing de
grees >= 0' contain a Km-trivial set [1]. Yet\, not every Turing degree c
ontains a Km-trivial set. We obtain a superset of the Km-trivial sets by
defining A to be almost trivial if there is a real number a such that K(A|
n) <= aK(n) +O(1). Every Km-trivial set is almost trivial. However\, the
Turing degree of a computably dominated ML-random cannot contain any almo
st trivial set. An interesting question is to determine which Turing degr
ees contain Km-trivial sets (or almost trivial sets). Recently\, this ques
tion has been considered for minimal Turing degrees. We also consider low
ness for monotone and a priory complexity. \n\n[1] Calhoun\, W.C.: T
riviality and minimality in the degrees of monotone complexity\, Journal o
f Logic and Computation 22\, 197-206 (2012).\n\n

[2] Nies\, Andre: Lowne
ss properties and randomness\, Advances in Mathematics 197\, 274-305 (2005
).
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151215T143000
DTEND;TZID=America/New_York:20151215T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=27076
SUMMARY:Logic Seminar - No Seminar This Week
DESCRIPTION:Seminar: Logic Seminar\nTitle: No Seminar This Week
END:VEVENT
END:VCALENDAR