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.

**(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*.

In preparation.

**(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

*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

*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:*

Wintersemester 2015/2016: Übungen zu Elemente der Mathematik

Übungsblatt 1: pdf

Übungsblatt 2: pdf

Übungsblatt 3: pdf

Übungsblatt 4: pdf --> Lösungen

Übungsblatt 5: pdf --> Lösungen

Übungsblatt 6: pdf --> Lösungen

Übungsblatt 7: pdf --> Lösungen

Übungsblatt 8: pdf --> Lösungen (von Leon Hendrian)
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Übungsblatt 9: pdf

Übungsblatt 10: pdf

Übungsblatt 11: pdf

Übungsblatt 12: pdf

Bonuspunkteblatt: pdf

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 (Introduction to Mathematical Logic, spring 2015):
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Old Exercises (Introduction to Mathematical Logic, autumn 2011):
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Reading Course in Set Theory info.

Old Exercises (Axiomatic Set Theory 1, spring 2011):
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Old Exercises (Axiomatic Set Theory 1, spring 2010):
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Old Exercises (Axiomatic Set Theory 1, spring 2009):
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Update log here.