

Gunter Fuchs
The College of Staten Island (CUNY)
Department of Mathematics
2800 Victory Boulevard
Staten Island, NY 10314
room 1S225
phone: 7189824182
math department: 7189823600
The Graduate Center (CUNY)
Mathematics Program
365 5th Avenue
New York, NY 10016
room 4432
phone: 2128178143
math program: 2128178530
Links:

Please send any questions or comments to:
Teaching
In the Spring 2021 Semester, I teach MTH 229 (Calculus Computer Lab) at CSI, online.
Research Interests
 Set Theory
 Inner Model Theory
 Forcing, Forcing Axioms, Iterated Forcing
Publications and Preprints
Please note that most of the preprints that are available here differ from the published versions.
Published

Arthur Apter, Shoshana Friedman and Gunter Fuchs.
More on HODsupercompactness.
Annals of Pure and Applied Logic 172(3): 21 pages (2021).
Preprint on the arXiv.

Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz and Ralf Schindler.
Innermodel reflection principles.
Studia Logica 108: 573595 (2020).
DOI: 10.1007/s11225019098607
Preprint available at the arXiv.

Gunter Fuchs.
Diagonal reflections on squares.
Archive for Mathematical Logic 58(12): 126 (2019).
DOI: 10.1007/s0015301806147
Here is an open access version (read only), and
here is a preprint.

Gunter Fuchs.
Subcomplete forcing principles and definable wellorders.
Mathematical Logic Quarterly 64(6):487504 (2018).
DOI: 10.1002/malq.201800008
Preprint: arXiv:1708.08167 [math.LO]

Gunter Fuchs and Ralf Schindler.
The solidity and nonsolidity of initial segments of the core model.
Journal of Symbolic Logic 83(3): 920938 (2018).
DOI: 10.1017/jsl.2018.45
Here is a preprint.

Gunter Fuchs and Kaethe Minden.
Subcomplete forcing, trees and generic absoluteness.
Journal of Symbolic Logic 83(3): 12821305 (2018).
DOI: 10.1017/jsl.2018.23
Preprint here and on the arXiv:1708.08170 [math.LO]

Gunter Fuchs.
Closure properties of parametric subcompleteness.
Archive for Mathematical Logic 57(78): 829852 (2018).
DOI: 10.1007/s001530180611x
Here is the online first version (read only), and
here is a preprint.

Gunter Fuchs and Assaf Rinot.
Weak square and stationary reflection.
Acta Mathematica Hungarica 155(2): 393405 (2018).
DOI: 10.1007/s1047401807898.
Here is the online first version (read only), and
here is a preprint. Also available on the arxiv.

Gunter Fuchs, Victoria Gitman and Joel David Hamkins.
Ehrenfeucht's lemma in set theory.
Notre Dame Journal of Formal Logic 59(3): 355370 (2018).
DOI: 10.1215/0029452720180007.
Preprint available at the arXiv.

Gunter Fuchs.
Hierarchies of forcing axioms, the continuum hypothesis and square principles.
Journal of Symbolic Logic 83(1): 256282 (2018).
DOI: 10.1017/jsl.2017.46
Here is a preprint.

Gunter Fuchs.
Hierarchies of (virtual) resurrection axioms.
Journal of Symbolic Logic 83(1): 283325 (2018).
DOI: 10.1017/jsl.2017.65
Here is a preprint (updated on 8/23/2017).

Gunter Fuchs.
The subcompleteness of Magidor forcing.
Archive for Mathematical Logic 57(34): 273284 (2018).
DOI: 10.1007/s0015301705681
Here is a read only version online (free access),
and here is a preprint.

Gunter Fuchs, Victoria Gitman and Joel David Hamkins.
Incomparable ω_{1}like models of set theory.
Mathematical Logic Quarterly 63 (12):6676 (2017).
DOI: 10.1002/malq.201500002
Preprint available at the arXiv.

Gunter Fuchs and Ralf Schindler.
Inner model theoretic geology.
Journal of Symbolic Logic 81(3):972996 (2016). DOI: 10.1017/jsl.2015.64
Here is a preprint.

Gunter Fuchs.
The stationarity of the collection of the locally regulars.
Archive for Mathematical Logic 54(5):725739 (2015). DOI: 10.1007/s0015301504378
Here is a preprint.

Gunter Fuchs, Joel David Hamkins and Jonas Reitz.
Settheoretic geology.
Annals of Pure and Applied Logic. 166(4):464501 (2015). DOI: 10.1016/j.apal.2014.11.004.
Preprint available on the arXiv.

Gunter Fuchs.
On sequences generic in the sense of Magidor.
Journal of Symbolic Logic 79(4):12861314 (2014).
DOI: 10.1017/jsl.2014.33.
Here is a preprint.

Gunter Fuchs.
Club degrees of rigidity and almost Kurepa trees.
Archive for Mathematical Logic 52(1): 4766 (2013).
DOI: 10.1007/s0015301203067.
Here is a preprint.

Gunter Fuchs and Philipp Lücke.
Iteratively changing the heights of automorphism towers.
Notre Dame Journal of Formal Logic 53(2):155174 (2012).
DOI: 10.1215/002945271715662.
Here is a preprint.

Gunter Fuchs.
λstructures and sstructures: translating the iteration strategies.
Annals of Pure and Applied Logic 162(9):710751 (2011).
DOI: 10.1016/j.apal.2011.02.002.
Here is a preprint.

Gunter Fuchs.
λstructures and sstructures: translating the models.
Annals of Pure and Applied Logic 162(4):257317 (2011).
DOI: 10.1016/j.apal.2010.08.003.
Here is a preprint.

Gunter Fuchs.
Generic embeddings associated to an indestructibly weakly compact cardinal.
Annals of Pure and Applied Logic 162(1):89105 (2010).
DOI: 10.1016/j.apal.2010.07.005.
Here is a preprint.

Gunter Fuchs, Itay Neeman, and Ralf Schindler.
A criterion for coarse iterability.
Archive for Mathematical Logic 49(4):447467 (2010).
This article is also available electronically on SpringerLink (open access, DOI: 10.1007/s0015301001800).

Gunter Fuchs.
Combined maximality principles up to large cardinals.
Journal of Symbolic Logic 74(3):10151046 (2009).
Here is a preprint.

Gunter Fuchs and Joel David Hamkins.
Degrees of rigidity for Souslin trees.
Journal of Symbolic Logic 74(2):423454 (2009).
Preprint available at the arXiv.

Gunter Fuchs.
Successor levels of the Jensen Hierarchy.
Mathematical Logic Quarterly 55(1):5369 (2009).
Here is a preprint.

Gunter Fuchs and Joel David Hamkins.
Changing the heights of automorphism towers by forcing with Souslin trees over L.
Journal of Symbolic Logic 73(2):614633 (2008).
Preprint available at the arXiv.

Gunter Fuchs.
Closed maximality principles: implications, separations and combinations.
Journal of Symbolic Logic 73(1):276308 (2008).
Here is a preprint.

Gunter Fuchs.
A characterization of generalized Příkrý sequences.
Archive for Mathematical Logic 44(8):935971 (2005).
Accepted

Gunter Fuchs.
Aronszajn tree preservation and bounded forcing axioms.
To appear in the Journal of Symbolic Logic. 16 pages. Submitted and accepted in 2020.
Preprint on the arXiv.

Gunter Fuchs and Chris LambieHanson.
Separating diagonal stationary reflection principles.
To appear in the Journal of Symbolic Logic, 32 pages (2020).
Preprint on the arXiv.

Gunter Fuchs.
Canonical fragments of the strong reflection principle.
Accepted for publication in the Journal of Mathematical Logic in 2020. Submitted in 2020. 48 pages.
Preprint on the arXiv.
Submitted

Gunter Fuchs and Corey Bacal Switzer.
Iteration theorems for subversions of forcing classes.
Submitted in 2020. 45 pages.
Preprint on the arXiv.
Other works

Gunter Fuchs.
λStrukturen und sStrukturen.
Dissertation (in German), Humboldt University Berlin. DOI: 10.18452/14903.
297 pages (2003).

Gunter Fuchs.
Eine Verallgemeinerung von Prikrys Forcing.
Master's Thesis (German Diplom, written in German), Humboldt University Berlin. Here is a copy.
78 pages (1998).
In preparation

Gunter Fuchs and Kaethe Minden.
Split principles, large cardinals, splitting families and split ideals.
Preprint on the arXiv.

Gunter Fuchs and Joel David Hamkins.
Boolean ultrapowers, the BukovskýDehornoy phenomenon, and iterated ultrapowers.
Here is a preprint.

Gunter Fuchs.
The strong Příkrý property.
Here is a preprint.
Talks

The subcomplete fragment of the Strong Reflection Principle
Carnegie Mellon University Mathematical Logic Seminar
September 29, 2020.

Canonical fragments of the Strong Reflection Principle
CUNY Virtual Set Theory Seminar
August 14, 2020.
This talk was recorded and can be watched on the NYLogic YouTube channel.

Relativizing strong reflection principles to forcing classes
15th international Luminy workshop in set theory, CIRM Luminy, France.
September 25, 2019.

Simultaneous exact reflection and mutual stationarity
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
September 13, 2019.

Ordinal diagonal reflection principles and squares
Seventh European Set Theory Conference, University of Vienna, Austria.
July 1, 2019.

Bounded forcing axioms and the preservation of wide Aronszajn trees
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
February 1, 2019.

Definable wellorderings of the reals from subcomplete forcing principles
Set Theory Seminar, University of Bonn, Germany.
January 15, 2019.

What is the bounded forcing axiom for countably closed forcing?
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
August 31, 2018.

Subversions of iterable forcing classes
First Girona conference on inner model theory, Girona (Catalonia).
July 19, 2018.

Determining the extent of weak Todorcevic square principles by reflecting diagonally
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
November 17, 2017.

Subcomplete forcing and its forcing principles
Set theory conference on the occasion of Ronald Jensen's 80th birthday, Münster, Germany.
August 3rd, 2017.
Slides and an overview diagram

Consequences of subcomplete forcing principles
CUNY Logic Workshop, CUNY Graduate Center, New York.
April 21, 2017.

Weak bounded forcing axioms and remarkably reflecting cardinals
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
March 3, 2017.

Hierarchies of forcing axioms
CUNY Logic Workshop, CUNY Graduate Center, New York.
November 4, 2016.

Boolean Ultrapowers in Set Theory
CUNY Logic Workshop, CUNY Graduate Center, New York.
February 5, 2016.

Boolean ultrapowers and the BukovskyDehornoy phenomenon
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
September 18, 2015.

Prikrytype sequences: a composition of interconnected results
The fifth European Set Theory Conference, Cambridge, UK.
August 27, 2015. Here is a video of the talk.

Settheoretic geology in the presence of an inner model with a Woodin cardinal
3rd Münster conference on inner model theory, the core model induction and hod mice, WWU Münster, Germany.
July 20, 2015.

News on the Solid Core
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
November 7, 2014.

Algebraicity versus Definability
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
April 25, 2014.

Prikrytype sequences, iterations and critical sequences
CUNY Logic Workshop, CUNY Graduate Center, New York.
November 8, 2013.

Characterizing Magidor Sequences
Rutgers Logic Seminar, Rutgers University, New Jersey.
September 16, 2013.

Magidor Sequences
Set Theory Seminar Seminar, Münster University, Germany.
July 9, 2013.

Constructing a Souslin almost Kurepa tree
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
March 23, 2012.

The Stationarity of the Collection of Local Aleph Ones
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
February 24, 2012.

On Changing Automorphism Tower Heights by Forcing
Rutgers Logic Seminar, Rutgers University, New Jersey.
February 20, 2012.

Settheoretic Geology and Canonical Inner Models
CUNY Logic Workshop, CUNY Graduate Center.
September 23, 2011.

Mysteries of the Generic Multiverse
Toronto Set Theory Seminar, Fields Institute, Toronto.
August 19, 2011.

Automorphisms of Souslin Trees
Summer Conference on General Topology and its Applications, The City College of New York.
July 27, 2011.

An Application of Almost Disjoint Coding
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
May 6, 2011.

Structural Consequences of AD I+II
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
September 3 and September 14, 2010.

Iterated Ultrapowers and Inner Models of Measurability I+II
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
April 23 and April 30, 2010.

Reflections on the Structure of the Generic Multiverse
Rutgers Logic Seminar, Rutgers University, New Jersey.
March 29, 2010.

Some recent forcing ideas
Lecture series held at Universidad
Autónoma Metropolitana, Unidad Iztapalapa in Mexico City.
January 11 to January 15, 2010.

An Invitation to Inner Model Theory
CUNY Set Theory Seminar, CUNY Graduate Center, New York.
November 6 to November 20, 2009.

Set Theoretic Geology meets Inner Model Theory
Miniworkshop on Fine Structure Theory, Oberwolfach, Germany.
November 10, 2009.

Maximality Principles and the Generic Multiverse
CUNY Logic Workshop, CUNY Graduate Center, New York.
September 25, 2009.

The Solovay Model
Talk at my Habilitation Colloquium, Münster University. This talk was aimed at general mathematicians.
July 22, 2009. By giving this talk, I completed my Habilitation.

Fixpunkte: Eine fixe Idee in der Mathematik
Talk at the Lange Nacht der Mathematik, Münster University. This talk was aimed at a general audience of nonmathematicians.
May 30, 2008. Due to public request, this talk can be downloaded in pdf format.

Closed Maximality Principles, Large Cardinals, etc.
CUNY Set Theory Seminar, The CUNY Graduate Center, New York.
February 29, 2008.

From Maximality Principles Via Weak Compactness to Generic Embeddings
Young Set Theory workshop in Bonn, Germany,
January 24, 2008.

Aspects of Indestructible Weak Compactness
Set Theory Workshop 2008 at the Mathematical Research Institute Oberwolfach, Germany,
January 15, 2008.

Maximality Principles for Closed Forcings
Logic Colloquium 2007 in Wroclaw, Poland
July 18, 2007. Due to public request, this talk can be downloaded in
pdf format.

Closed Maximality Principles and Large Cardinals
First European Set Theory Meeting in Bedlewo, Poland
July 12, 2007. This talk can also be downloaded in pdf format.

Maximality Principles for Closed Forcings
Lecture at the Set Theory Seminar in Bonn, Germany
April 10, 2007.

Degrees of Rigidity and Changing the Heights of
Automorphism Towers
Colloquium Logicum 2006/Annual
Meeting of the German Mathematicians' Association in Bonn, Germany
September 22, 2006

Degrees of Rigidity for Souslin Trees
MiniWorkshop on Fine Structure and Inner Models at
the Mathematical Research Institute Oberwolfach, Germany
May 1, 2006.

λStructures and sStructures
Lecture at the Computational Prospects of Infinity program at the National University of Singapore
July 8, 2005.

Degrees of Rigidity for Souslin Trees
Lecture at the Computational Prospects of Infinity program at the
National University of Singapore
June 24, 2005.

λStrukturen und sStrukturen
BerlinPotsdam Logic Colloquium, Berlin, Germany
December 9, 2002

MitchellSteel Mice versus FriedmanJensen Mice
MiniWorkshop on Fine Structure Theory at the Mathematical Research Institute Oberwolfach, Germany
February 26, 2001

Characterizing Generalized Příkrý Sequences
Lecture at the Set Theory Seminar, Bonn University, Germany
June 29, 2000

A Generalization of Příkrý Forcing
BerlinPotsdam Logic Colloquium, Berlin, Germany
January 10, 2000.
Vitae
 Born in Västanfors, Sweden
 Starting August 2013: Associate Professor at CSI / CUNY
 December 2011: Joined the doctoral faculty at the Ph.D. Program in Mathematics of the CUNY Graduate Center
 Starting September 2009: Assistant Professor at CSI / CUNY
 July 22, 2009: Habilitation
 Dec. 2004  August 2009: Assistant Professor at Münster University (German wissenschaftlicher Assistent), Germany
 June 2003: Received Ph. D. in Mathematics, supervisor: Ronald Jensen (Humboldt University Berlin)
 Oct. 1998  November 2004: DFG fellow in Berlin/Münster
 Sept. 1998: Received Diploma (M. Sc.) in Mathematics (Humboldt University Berlin)
 Oct. 1995  Sept. 1998: Graduate Assistant (Humboldt University Berlin)