W. Hugh Woodin | Academic Influence

W. Hugh Woodin's AcademicInfluence.com Rankings

W. Hugh Woodin

Mathematics

#272

World Rank

#586

Historical Rank

#127

USA Rank

Set Theory

#3

World Rank

#9

Historical Rank

#1

USA Rank

Measure Theory

#504

World Rank

#711

Historical Rank

#208

USA Rank

mathematics Degrees

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Mathematics

W. Hugh Woodin's Degrees

PhD Mathematics University of California, Berkeley

Why Is W. Hugh Woodin Influential?

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According to Wikipedia, William Hugh Woodin is an American mathematician and set theorist at Harvard University. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinals, the Woodin cardinals, bear his name. In 2023, he was elected to the National Academy of Sciences.

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W. Hugh Woodin's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal (1999) (355)
Large Cardinals from Determinacy (2010) (124)
Supercompact cardinals, sets of reals, and weakly homogeneous trees. (1988) (116)
The Structure of σ-Ideals of Compact Sets (1987) (105)
An Introduction to Independence for Analysts (1987) (98)
The generalized continuum hypothesis can fail everywhere (1991) (87)
Suitable Extender Models I (2010) (84)
The Continuum Hypothesis, Part I (2001) (77)
Suitable Extender Models II: beyond ω-Huge (2011) (58)
Equivalence of partition properties and determinacy. (1983) (57)
In Search of ultimate-l the 19th Midrasha Mathematicae Lectures (2017) (55)
Definability in the Turing degrees (1986) (53)
On the Consistency Strength of Projective UNI Formization (1982) (52)
The axiom of determinacy, strong partition properties and nonsingular measures (1981) (47)
HOD as a core model (2016) (46)
Small forcing creates neither strong nor Woodin cardinals (1998) (43)
Super-Real Fields: Totally Ordered Fields with Additional Structure (1996) (36)
Set Theory, Arithmetic, and Foundations of Mathematics: The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture (2011) (36)
The Continuum Hypothesis , Part II (2001) (31)
The Borel Conjecture (1990) (30)
LARGE CARDINALS BEYOND CHOICE (2019) (26)
Complexity of Reals in Inner Models of Set Theory (1995) (25)
THE GROUND AXIOM IS CONSISTENT WITH V ≠ HOD (2008) (25)
Definability in the enumeration degrees (1997) (24)
The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal (2004) (24)
On the consistency strength of the inner model hypothesis (2007) (24)
Ad and the uniqueness of the supercompact measures on Pω1(λ) (1983) (22)
Infinity: The Realm of the Infinite (2011) (22)
A barren extension (1985) (21)
Saturation of the closed unbounded filter on the set of regular cardinals (1985) (19)
Mice with finitely many Woodin cardinals from optimal determinacy hypotheses (2019) (19)
Some consistency results in ZFC using AD (2020) (18)
Large cardinal axioms and independence: The continuum problem revisited (1994) (18)
Ranks of differentiable functions (1986) (18)
Incompatible Ω-Complete Theories (2009) (16)
Strong Axioms of Infinity and the Search for V (2011) (16)
Computational prospects of infinity Part II, Presented talks / (2008) (16)
Beyond Σ ∼ 2 1 Absoluteness (2002) (16)
DETERMINACY AND JÓNSSON CARDINALS IN L(ℝ) (2013) (15)
Kurt Gödel and the Foundations of Mathematics: The Transfinite Universe (2011) (13)
Forcing the failure of CH by adding a real (1984) (12)
A Discontinuous Homomorphism from C(X) without CH (1993) (12)
The Jensen Covering Property (1997) (11)
The universal finite set (2017) (10)
Generic codes for uncountable ordinals, partition properties, and elementary embeddings (2008) (10)
Infinity: A Potential Subtlety Concerning the Distinction between Determinism and Nondeterminism (2011) (10)
Infinity: New Research Frontiers (2014) (10)
Games, Scales, and Suslin Cardinals: The Cabal Seminar, Volume I: Weakly homogeneous trees (2008) (9)
The Ω conjecture (2001) (8)
A Strong Boundedness Theorem for Dilators (1991) (8)
E-recursion, forcing and C*-algebras (2014) (7)
A tt VERSION OF THE POSNER-ROBINSON THEOREM (2008) (7)
Games, Scales, and Suslin Cardinals: The Cabal Seminar, Volume I: The axiom of determinacy, strong partition properties, and nonsingular measures (2008) (6)
sets of reals (1997) (6)
The cardinals below |[omega1] (2006) (6)
Computational prospects of infinity Part I, Tutorials / (2008) (6)
Open class determinacy is preserved by forcing (2018) (5)
Strong Axioms of Infinity and the Debate About Realism (2014) (5)
1\ sets of reals (1997) (5)
DETERMINACY AND JÓNSSON CARDINALS IN L(R) (2014) (5)
TUTORIAL OUTLINE: SUITABLE EXTENDER SEQUENCES (2008) (4)
Extending Partial Orders to Dense Linear Orders (1998) (4)
Forcing, Iterated Ultrapowers, and Turing Degrees (2015) (4)
$\underset{\tilde}{\Delta}^1_n$ Sets of Reals (1997) (3)
Infinity and truth (2014) (3)
The universe constructed from a sequence of ordinals (1996) (3)
P-points in Qmax models (2003) (3)
Real Determinacy and Real Blackwell Determinacy (2010) (3)
3 The nonstationary ideal (2010) (3)
Concept Calculus: Much Better Than (2011) (2)
Notes on the Concept of the Infinite in the History of Western Metaphysics (2011) (2)
A (Partially) Skeptical Response to Hart and Russell (2011) (2)
The Weak Ultrafilter Axiom (2016) (2)
AD and J\'onsson cardinals in L(R) (2013) (2)
Turing Determinacy and Suslin sets (2022) (1)
\undertilde₂¹ without sharps (1996) (1)
Beyond X \ Absoluteness (2002) (1)
An Introduction to Independence for Analysts: Forcing (1987) (1)
Cosmological Intimations of Infinity (2011) (1)
Two weak consequences of 0# (1985) (1)
9 Extensions of L(Γ, ℝ). 9.5 Weak and Strong Reflection Principles (1999) (0)
10 Further results. 10.3 Bounded forms of Martin’s Maximum (1999) (0)
6 ℙmax variations (2010) (0)
Limit computability and constructive measure (0)
AD and the uniqueness of the supercompact measures on ℘ꞷ1 (λ) (2020) (0)
Martin's Axiom (1987) (0)
10 Further results. 10.5 Ω-logic and the Continuum Hypothesis (1999) (0)
Beyond $\underTilde{\Sigma}^2_1$ absoluteness (2002) (0)
9 Extensions of L(Γ, ℝ). 9.1 AD+ (1999) (0)
Woodin's condition (1987) (0)
Chapter 12: Structure of Compact Spaces (2014) (0)
Chapter 7: The Side-condition Method (2014) (0)
Atlanta Marriott Marquis, Atlanta, Georgia January 7–8, 2005 (2005) (0)
Chapter 1: Baire Category Theorem and the Baire Category Numbers (2014) (0)
SPONSORED BY THE ASSOCIATION FOR SYMBOLIC LOGIC (2013) (0)
‘TUNNEL IN THE DESERT’ AN UNDERGROUND EXHIBIT FOR NOCTURNAL ANIMALS (1962) (0)
9 Extensions of L(Γ, ℝ). 9.4 Chang’s Conjecture (1999) (0)
Chapter 4: Consequences in Measure Theory (2014) (0)
10 Further results. 10.1 Forcing notions and large cardinals (1999) (0)
Incompatible Omega-complete theories (2009) (0)
Equivalence of partition properties and determinacy ( set theory / descriptive set theory / constructible from the reals universe (0)
~Delta1n Sets of Reals (1997) (0)
Homomorphisms from algebras of continuous functions (1987) (0)
10 Further results. 10.7 The Effective Singular Cardinals Hypothesis (1999) (0)
Without Sharps (1995) (0)
Chapter 14: Five Cofinal Types (2014) (0)
9 Extensions of L(Γ, ℝ). 9.7 Ideals on ω2 (1999) (0)
Chapter 6: The S-spaces and the L-spaces (2014) (0)
Chapter 17: Reflection Principles (2014) (0)
8 ♣ principles for ω1. 8.2 ℙ♣NSmax (1999) (0)
Chapter 5: Variations on the Souslin Hypothesis (2014) (0)
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.6 Null sets and the nonstationary ideal (1999) (0)
Pi13 Sets and Pi13 Singletons (1999) (0)
Logic and Mathematics (2010) (0)
Chapter 9: Coherent and Lipschitz Trees (2014) (0)
Delta-1-2 Without Sharps (1995) (0)
8 ♣ principles for ω1. 8.3 The principles, ♣+NS and ♣++NS (1999) (0)
10 Further results. 10.4 Ω-logic (1999) (0)
2002 Annual Meeting of the Association for Symbolic Logic (2003) (0)
9 Extensions of L(Γ, ℝ) (2010) (0)
10 Further results. 10.2 Coding into L(P(ω1)) (1999) (0)
8 ♣ principles for ω 1 (2010) (0)
10 Further results. 10.6 The Axiom ( (1999) (0)
Chapter 15: Five Linear Orderings (2014) (0)
Π13 sets and π13 singletons (1999) (0)
sets and singletons (1999) (0)
Chapter 8: Ideal Dichotomies (2014) (0)
9 Extensions of L(Γ, ℝ). 9.6 Strong Chang’s Conjecture (1999) (0)
8 ♣ principles for ω1. 8.1 Condensation Principles (1999) (0)
An Introduction to Independence for Analysts: Partial orders, Boolean algebras, and ultraproducts (1987) (0)
Chapter 11: Biorthogonal Systems (2014) (0)
The Weak Ultrafilter Axiom (2015) (0)
10 Further results (2010) (0)
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.4 Weak Kurepa trees and ℚmax (1999) (0)
6 ℙmax variations. 6.3 Nonregular ultrafilters on ω1 (1999) (0)
Chapter 16: Cardinal Arithmetic and (2014) (0)
Andou, Y., Church–Rosser property of a simple reduction for full first-order classical natural deduction (1–3) 225–237 Bridges, D. and Vıˆt-a, L., Apartness spaces as a framework for constructive topology (1–3) 61–83 Di Nasso, M. and Hrbacek, K., Combinatorial principles in (2003) (0)
4 The ℙmax-extension (2010) (0)
(set theory/descriptive set theory/constructible from the reals univer (2016) (0)
7 Conditional variations (1999) (0)
Chapter 10: Applications to the S-space Problem and the von Neumann Problem (2014) (0)
Independence in set theory (1987) (0)
Chapter 13: Ramsey Theory on Ordinals (2014) (0)
The strength of the Inner Model Hypothesis (2007) (0)
Chapter 2: Coding Sets by the Real Numbers (2014) (0)
9 Extensions of L(Γ, ℝ). 9.2 The ℙmax-extension of L(Γ, ℝ) (1999) (0)
Chapter 3: Consequences in Descriptive Set Theory (2014) (0)
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.5 KTℚmax (1999) (0)
$Pi^13$ Sets and $Pi^13$ Singletons (1999) (0)
6 ℙmax variations. 6.1 2ℙmax (1999) (0)
Notes for the IMS Summer School in Mathematical Logic-2019 (2019) (0)
Gaps in ordered sets (1987) (0)
Infinity: Perspectives on Infinity from Physics and Cosmology (2011) (0)

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