Peter Holy


Peter Holy

E-Mail: pholy@math.uni-bonn.de
Phone: +49 228 73 62347
Office: N1.014, Mathematisches Institut der Universität Bonn

I am a postdoc at the University of Bonn.


Research Interests: I am working in set theory with a focus on forcing, definability and large cardinals.


Publications

(with Philipp Lücke) Internal large cardinals.
In preparation. talk slides

Further Small Embedding Characterizations for Large Cardinals.
In preparation.

(with Philipp Lücke and Ana Njegomir) Characterizing Large Cardinals through Neeman's pure side condition forcing.
In preparation.

(with Philipp Lücke and Ana Njegomir) Small Embedding Characterizations for Large Cardinals.
Submitted, 2017. pdf talk slides

(with Victoria Gitman, Joel Hamkins, Philipp Schlicht and Kameryn Williams) The exact Strength of the Class Forcing Theorem.
Submitted, 2017. pdf

(with Regula Krapf and Philipp Schlicht) Sufficient conditions for the forcing theorem, and turning proper classes into sets.
Submitted, 2017. pdf

(with Philipp Schlicht) A Hierarchy of Ramsey-like cardinals.
Submitted, 2017. pdf

(with Regula Krapf and Philipp Schlicht) Characterizations of Pretameness and the Ord-cc.
Accepted for Annals of Pure and Applied Logic, 2017. pdf

(with Regula Krapf, Philipp Lücke, Ana Njegomir and Philipp Schlicht) Class Forcing, the Forcing Theorem and Boolean Completions.
Journal of Symbolic Logic 81, no. 4, pp. 1500-1530, 2016. pdf talk slides

Sigma_1-Wellorders without Collapsing.
Archive for Mathematical Logic 54, issue 3, pp 453-462, 2015. pdf talk slides

(with Philipp Lücke) Simplest possible locally definable Wellorders.
Fundamenta Mathematicae 236, pp. 101-139, 2017. pdf talk slides

(with David Asperó and Philipp Lücke) Forcing lightface Definable Wellorders without the GCH.
Annals of Pure and Applied Logic 166, no. 5, pp. 553-582, 2015. pdf, David Asperó's talk slides

(with Philip Welch and Liuzhen Wu) Local Club Condensation and L-likeness.
Journal of Symbolic Logic 80, no. 4, pp. 1361-1378, 2015. pdf, talk slides

(with Philipp Lücke) Locally Sigma_1-definable Wellorders of H(kappa^+).
Fundamenta Mathematicae 226, pp 221-236, 2014. pdf, talk slides

(with Sy-David Friedman and Philipp Lücke) Large Cardinals and Lightface Definable Wellorders without GCH.
Journal of Symbolic Logic 80, issue 1, pp 251-284, 2015. pdf, talk slides

(with Sy-David Friedman) A Quasi Lower Bound on the Consistency Strength of PFA.
Transactions of the AMS 366, pp 4021-4065, 2014. pdf, talk slides

(with Sy-David Friedman) Condensation and Large Cardinals.
Fundamenta Mathematicae 215, no. 2, pp 133-166, 2011. pdf, info

Dissertation: Condensation and Large Cardinals.
(2010, advisor: Sy D. Friedman) pdf, info

Masters Thesis: Absoluteness Results in Set Theory.
(2007, advisor: Sy D. Friedman) pdf


Unpublished Notes

(with Regula Krapf and Philipp Schlicht) Separation in Class Forcing Extensions.
(2017) pdf

A generalization of the notion of bounded degree for infinite graphs.
(2014) pdf

PFA and Class Forcing.
(2013) pdf

Canonical Function Coding over a Stationary Set.
(2013) pdf, info

Condensation and Large Cardinals - A Simplified Version of my Dissertation.
(2013) pdf, info


Upcoming Talks

Nothing scheduled at the moment.


Past Talks

Large Cardinals

A Hierarchy of Ramsey-like cardinals
Bristol Set Theory Seminar, 07.03.2017

Small embedding characterizations for large cardinals, and internal large cardinals
Bonn Logic Seminar, 09.05.2016; Young Set Theory Workshop, Copenhagen, 16.06.2016; Kurt Gödel Research Center, 06.04.2017 --> pdf


Class Forcing

How to and how not to turn proper classes into sets
Bonn Logic Seminar, 24.10.2016

Class Forcing and Pretameness
Hamburg Logic Seminar, 30.05.2016

Failures of the Forcing Theorem
European Set Theory Conference, Cambridge, 25.08.2015 --> pdf

Non-pretame Class Forcing and the Forcing Theorem, the axioms of ZFC and non-definable Class Forcing
Kurt Gödel Research Center, Vienna, 27.05.2015

The Dark Side of Class Forcing
Bristol Logic Seminar, 10.03.2015


Locally Definable Wellorders

Forcing lightface definable Wellorders without the GCH
Bonn Logic Seminar, 09.11.2015

Delta^1_1 subsets of the generalized Baire Space
Amsterdam workshop on Set Theory, 03.11.2014 --> pdf

Simplest Possible Wellorders of H(kappa^+)
Winter School in Abstract Analysis, section Set Theory and Topology, Hejnice, 26.01.2014; Bonn Logic Seminar, 19.02.2014; Bristol Logic Seminar, 18.03.2014

Locally Sigma_1-definable wellorders of H(kappa^+)
ESI Workshop on Forcing and Large Cardinals, Vienna, 23.09.2013

Large Cardinals and lightface definable Wellorders without the GCH
Kurt Gödel Research Center, Vienna, 10.01.2013; Bristol Logic Seminar, 11.03.2013 --> pdf


Condensation and the Outer Model Programme

Condensation does not imply Square
Inner and Outer Model Theory Workshop, Bristol, 06.07.2014; Bonn Logic Seminar, 20.04.2015; Münster Set Theory Seminar, 11.06.2015; Logic Colloquium, Helskinki, 03.08.2015 --> pdf

The Outer Model Programme
Oxford Logic Seminar, 07.02.2013; Norwich Pure Maths Seminar, 28.04.2014 --> pdf

L-like Models with Large Cardinals and a quasi lower Bound on the Consistency Strength of PFA.
PhD Colloquium Paderborn, 13.09.2012; Bristol Logic Seminar, 28.11.2012; Bonn Logic Seminar, 08.04.2013; Young Set Theory Workshop Oropa, 12.07.2013 --> pdf


General Mathematics Audience Talks

Surreal Numbers
Basic Notions Seminar, Bonn, 25.10.2016 (following slides by Yurii Khomskii)

Forcing: How to prove Unprovability
Basic Notions Seminar, Bonn, 18.11.2015 (Part II of a two-part talk, part I by Regula Krapf).


Teaching

Past Teaching

at the University of Bonn:

autumn 2015: Exercises for Elements of Mathematics

spring 2015:
Seminar in Mathematical Logic / Graduate Seminar in Set Theory (with Peter Koepke)
Exercises for Introduction to Mathematical Logic
Logic Bachelor thesis seminar (with Peter Koepke and Philipp Lücke)

autumn 2014: Exercises for Elements of Mathematics

at the University of Bristol:

2013/2014: Mathematics Tutorials for 1st year students (Analysis, Group Theory, Number Theory)
2012/2013: Mathematics Tutorials for 1st year students (Analysis, Group Theory, Number Theory)

at the Kurt Gödel Research Center for Mathematical Logic, Vienna:

autumn 2011:
Reading Course in Set Theory
Exercises for Introduction to Mathematical Logic.

spring 2011: Exercises for Axiomatic Set Theory 1.
spring 2010: Exercises for Axiomatic Set Theory 1.
spring 2009: Exercises for Axiomatic Set Theory 1.
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Old Exercises (Elements of Mathematics, autumn 2015): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
Old Exercises (Introduction to Mathematical Logic, spring 2015): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Old Exercises (Introduction to Mathematical Logic, autumn 2011): 1, 2, 3, 4, 5, 6, 7, 8, 9.
Reading Course in Set Theory info.
Old Exercises (Axiomatic Set Theory 1, spring 2011): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Old Exercises (Axiomatic Set Theory 1, spring 2010): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Old Exercises (Axiomatic Set Theory 1, spring 2009): 1, 2, 3, 4, 5, 6, 7, 8.


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