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.

Some more specific topics in my recent research include forcing Condensation principles together with or without other properties of the constructible universe, forcing (simple) locally definable wellorders without GCH (that is definable wellorders of H(kappa^+) when 2^kappa>kappa^+), non-pretame class forcing and I'm very interested in the construction of nonstandard forcing iterations.

Publications

**(with Victoria Gitman, Joel Hamkins, Philipp Schlicht and Kameryn Williams) ***The Strength of the Forcing Theorem*.

In preparation.

**(with Regula Krapf and Philipp Schlicht) ***Turning proper classes into sets in class forcing extensions*.

In preparation.

**(with Philipp Lücke) ***Collapsing, Definability and Applications*.

In preparation.

**(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 Philipp Schlicht) ***A Hierarchy of Ramsey-like cardinals*.

Submitted, 2017. pdf

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

Submitted, 2016.

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