Peter Holy

**E-Mail:** maxph@bristol.ac.uk
**Phone:** +44 (0)117 95 - 45614
**Office:** 2.16, Howard House

I am a research assistant at the University of Bristol.

Workshop -> Inner and Outer Model Theory

**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^+) and, on a technical level, I'm very interested in the construction of nonstandard forcing iterations.

Publications

*A generalization of the notion of bounded degree for infinite graphs*.

Submitted to the Israel Journal of Mathematics. pdf

*Many Sigma_1-wellorders, failures of the GCH and large cardinals*.

Submitted to the Archive for Mathematical Logic. pdf

**(with Philipp Lücke) ***Simplest possible locally definable Wellorders.*

Submitted to Fundamenta Mathematicae. pdf talk slides

**(with David Asperó and Philipp Lücke) ***Forcing lightface Definable Wellorders without the GCH.*

Submitted to the Annals of Pure and Applied Logic. pdf, David Asperó's talk slides

**(with Philip Welch and Liuzhen Wu) ***Local Club Condensation and L-likeness.*

Submitted to the Journal of Symbolic Logic. pdf, talk slides

**(with Philipp Lücke) ***Locally Sigma_1-definable Wellorders of H(kappa^+).*

Fundamenta Mathematicae 226, pp 221-236, 2014. pdf, talk slides

*PFA and Class Forcing.*

Submitted to Mathematical Logic Quarterly, 2014. pdf

**(with Sy-David Friedman and Philipp Lücke) ***Large Cardinals and Lightface Definable Wellorders without GCH.*

Accepted for the Journal of Symbolic Logic, 2013. 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Unpublished Notes

*Canonical Function Coding over a Stationary Set.*

(2013) pdf, info

*Condensation and Large Cardinals - A Simplified Version of my Dissertation.*

(2013) pdf, info

Current Projects

*Local Club Condensation and a precipitous ideal on omega_1*.

**(with Philipp Lücke) ***Collapsing, definability and applications*.

Upcoming Talks

*Delta^1_1 subsets of the generalized Baire Space.*

Amsterdam workshop on Set Theory, November 3rd and 4th, 2014

Slides for Talks

*Condensation does not imply Square*

Inner and Outer Model Theory Workshop, Bristol, 06.07.2014 --> 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 --> pdf

*Locally Sigma_1-definable wellorders of H(kappa^+)*

ESI Workshop on Forcing and Large Cardinals, Vienna, 23.09.2013 --> pdf (however you are advised to look at the slides for the talk on Simplest Possible Wellorders (pdf) instead as it is basically an improved and extended version of this talk)

*The Outer Model Programme*

Oxford Logic Seminar, 07.02.2013; Norwich Pure Maths Seminar, 28.04.2014 --> pdf

*Large Cardinals and lightface definable Wellorders without GCH*

Kurt Gödel Research Center, Vienna, 10.01.2013; Bristol Logic Seminar, 11.03.2013 --> 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

----> Collection of Oberwolfach Set Theory Workshop 2011 slides

**Teaching:**

**Past Teaching**

*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, 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.