Joel David Hamkins | Academic Influence

Joel David Hamkins's AcademicInfluence.com Rankings

Joel David Hamkins

Mathematics

#576

World Rank

#1091

Historical Rank

#257

USA Rank

Set Theory

#7

World Rank

#14

Historical Rank

#5

USA Rank

Measure Theory

#1158

World Rank

#1478

Historical Rank

#420

USA Rank

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Mathematics

Joel David Hamkins's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics Princeton University

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Why Is Joel David Hamkins Influential?

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According to Wikipedia, Joel David Hamkins is an American mathematician and philosopher who is O'Hara Professor of Philosophy and Mathematics at the University of Notre Dame. He has made contributions in mathematical and philosophical logic, set theory and philosophy of set theory , in computability theory, and in group theory.

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Joel David Hamkins'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

Infinite Time Turing Machines (1998) (326)
THE SET-THEORETIC MULTIVERSE (2011) (141)
Extensions with the approximation and cover properties have no new large cardinals (2003) (116)
The Lottery Preparation (1998) (116)
Gap forcing (1998) (88)
Gap Forcing: Generalizing the Lévy-Solovay Theorem (1999) (82)
Set-theoretic geology (2011) (77)
A simple maximality principle (2000) (74)
The modal logic of forcing (2005) (74)
What is the theory ZFC without power set? (2011) (65)
The Halting Problem Is Decidable on a Set of Asymptotic Probability One (2005) (51)
Small forcing creates neither strong nor Woodin cardinals (1998) (43)
Small forcing makes any cardinal superdestructible (1998) (42)
Destruction or Preservation as You Like It (2016) (42)
Infinite Time Turing Machines With Only One Tape (1999) (41)
The Hierarchy of Equivalence Relations on the Natural Numbers Under Computable Reducibility (2011) (39)
A class of strong diamond principles (2002) (36)
Fragile measurability (1994) (35)
Resurrection axioms and uplifting cardinals (2013) (33)
Well-founded Boolean ultrapowers as large cardinal embeddings (2012) (33)
Post's problem for supertasks has both positive and negative solutions (1998) (33)
A Natural Model of the Multiverse Axioms (2010) (32)
Indestructibility and the level-by-level agreement between strong compactness and supercompactness (2001) (31)
Generalizations of the Kunen inconsistency (2011) (28)
Structural connections between a forcing class and its modal logic (2012) (26)
Pointwise definable models of set theory (2011) (25)
THE GROUND AXIOM IS CONSISTENT WITH V ≠ HOD (2008) (25)
Is the Dream Solution of the Continuum Hypothesis Attainable? (2012) (25)
Set-theoretic mereology (2016) (25)
The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal (2004) (24)
Superstrong and other large cardinals are never Laver indestructible (2013) (24)
Universal Indestructibility (1998) (24)
Canonical seeds and Prikry trees (1997) (24)
Diamond (on the regulars) can fail at any strongly unfoldable cardinal (2004) (24)
Moving Up and Down in the Generic Multiverse (2012) (23)
Large cardinals with few measures (2006) (22)
THE EXACT STRENGTH OF THE CLASS FORCING THEOREM (2017) (21)
Degrees of rigidity for Souslin trees (2006) (21)
The Set-theoretic Multiverse : A Natural Context for Set Theory( Mathematical Logic and Its Applications) (2011) (21)
THE MODAL LOGIC OF SET-THEORETIC POTENTIALISM AND THE POTENTIALIST MAXIMALITY PRINCIPLES (2017) (20)
Superdestructibility: A dual to Laver's indestructibility (1996) (20)
Tall cardinals (2009) (20)
Indestructible Strong Unfoldability (2010) (19)
A multiverse perspective on the axiom of constructiblity (2012) (19)
Every group has a terminating transfinite automorphism tower (1998) (18)
P != NP cap co-NP for Infinite Time Turing Machines (2005) (18)
Every Countable Model of Set Theory embeds into its Own Constructible Universe (2012) (18)
Open determinacy for class games (2015) (18)
Some Second Order Set Theory (2009) (17)
INFINITE TIME COMPUTABLE MODEL THEORY (2006) (16)
With infinite utility, more needn't be better (2000) (15)
Unfoldable cardinals and the GCH (1999) (15)
Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata (1999) (14)
The Wholeness Axioms and V=HOD (1999) (14)
The modal logic of arithmetic potentialism and the universal algorithm (2018) (14)
Exactly controlling the non-supercompact strongly compact cardinals (2003) (14)
Algebraicity and Implicit Definability in Set Theory (2013) (13)
Inner models with large cardinal features usually obtained by forcing (2011) (12)
Large cardinals need not be large in HOD (2014) (12)
Effective model theory: approach via σ-definability (2013) (12)
Borel structures: a brief survey (2013) (12)
A model of the generic Vopěnka principle in which the ordinals are not Mahlo (2017) (12)
Changing the Heights of Automorphism Towers (1997) (12)
Utilitarianism in Infinite Worlds (2000) (11)
SATISFACTION IS NOT ABSOLUTE (2013) (11)
Upward closure and amalgamation in the generic multiverse of a countable model of set theory (2015) (11)
P f �= NP f for almost all f (2008) (11)
Infinite Time Turing Machines: Supertask Computation (2002) (11)
Strongly uplifting cardinals and the boldface resurrection axioms (2014) (11)
Infinite Time Decidable Equivalence Relation Theory (2009) (11)
The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $${\theta}$$θ-supercompact (2013) (10)
A Survey of Infinite Time Turing Machines (2007) (10)
The rearrangement number (2016) (10)
Pf ≠ NPf for almost all f (2003) (10)
The universal finite set (2017) (10)
Transfinite Game Values in Infinite Chess (2013) (9)
Infinitary Computability with Infinite Time Turing Machines (2005) (9)
Supertask computation (2002) (9)
Ehrenfeucht's Lemma in Set Theory (2015) (8)
The mate-in-n problem of infinite chess is decidable (2012) (8)
Post's Problem for ordinal register machines: An explicit approach (2009) (8)
Post's Problem for Ordinal Register Machines (2007) (8)
Effective mathematics of the uncountable (2013) (7)
THE Σ1-DEFINABLE UNIVERSAL FINITE SEQUENCE (2021) (6)
How Tall is the Automorphism Tower of a Group (1998) (6)
Changing the heights of automorphism towers by forcing with Souslin trees over L (2007) (6)
The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph _2$ or $\aleph _3$ (2008) (5)
The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme (2016) (5)
Open class determinacy is preserved by forcing (2018) (5)
The rigid relation principle, a new weak choice principle (2011) (5)
The set-theoretic universe $V$ is not necessarily a class-forcing extension of HOD (2017) (5)
Set-theoretic blockchains (2018) (4)
Infinite Time Turing Machines and an Application to the Hierarchy of Equivalence Relations on the Reals (2011) (4)
The least weakly compact cardinal can be unfoldable, weakly measurable and nearly θ -supercompact (2015) (4)
Inner-Model Reflection Principles (2017) (4)
The complexity of quickly decidable ORM-decidable sets (2007) (4)
Incomparable ω1‐like models of set theory (2017) (4)
New Inconsistencies in Infinite Utilitarianism: is Every World Good, Bad or Neutral? (2002) (4)
THE IMPLICITLY CONSTRUCTIBLE UNIVERSE (2017) (4)
A Position in Infinite Chess With Game Value ω4 (2017) (4)
Extending Kleene ’ s O Using Infinite Time Turing Machines , or How With Time She Grew (2007) (3)
P is not equal to NP intersect coNP for Infinite Time Turing Machines (2003) (3)
ZFC PROVES THAT THE CLASS OF ORDINALS IS NOT WEAKLY COMPACT FOR DEFINABLE CLASSES (2016) (3)
BI-INTERPRETATION IN WEAK SET THEORIES (2020) (3)
Singular cardinals and strong extenders (2012) (3)
Computable Quotient Presentations of Models of Arithmetic and Set Theory (2017) (3)
The Complexity of Quickly ORM-Decidable Sets (2007) (3)
The halting problem is almost always decidable (2006) (2)
The inclusion relations of the countable models of set theory are all isomorphic (2017) (2)
Kelley–Morse set theory does not prove the class Fodor principle (2019) (2)
The subseries number (2018) (2)
The foundation axiom and elementary self-embeddings of the universe (2013) (2)
The role of the foundation axiom in the Kunen inconsistency (2013) (2)
REFLECTION IN SECOND-ORDER SET THEORY WITH ABUNDANT URELEMENTS BI-INTERPRETS A SUPERCOMPACT CARDINAL (2022) (2)
Superdestructibility: a dual to the Laver preparation (1998) (2)
Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength (2022) (1)
Infinite Wordle and the Mastermind numbers (2022) (1)
A Generalization of the Gap Forcing Theorem (2003) (1)
Boolean ultrapowers, the Bukovsky-Dehornoy phenomenon, and iterated ultrapowers (2017) (1)
Transfinite game values in infinite draughts (2021) (1)
Pf= NPf almost everywhere (2003) (1)
Structural connections between a forcing class and its modal logic (2015) (1)
Every countable model of arithmetic or set theory has a pointwise-definable end extension (2022) (1)
When does every definable nonempty set have a definable element? (2017) (1)
Moschovakis Yiannis N.. Notes on set theory . Undergraduate texts in mathematics. Springer-Verlag, New York, Berlin, Heidelberg, etc., 1994, xiv + 272 pp. (1997) (0)
Superstrong and other large cardinals are never Laver indestructible (2015) (0)
Rearrangements (2019) (0)
Topological models of arithmetic (2018) (0)
Is the twin prime conjecture independent of Peano Arithmetic? (2021) (0)
Incomparable $\omega_1$-like models of set theory (2015) (0)
P^f is not equal to NP^f for almost all f (2002) (0)
The Ground Axiom (2016) (0)
Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account (2022) (0)
Fe b 20 06 INFINITE TIME COMPUTABLE MODEL THEORY (2018) (0)
CLASSIFICATION AND SUMMARY OF RESEARCH (2013) (0)
Infinitary computability with infinite time (2005) (0)
Set-theoretic blockchains (2019) (0)
A model of the generic Vopěnka principle in which the ordinals are not Mahlo (2018) (0)
REVIEWS-Lectures in Logic and Set Theory, vols. I & II (2005) (0)
A position in infinite chess with game value $\omega^4$ (2015) (0)
Resurrection axioms and uplifting cardinals (2014) (0)
The Vop\v{e}nka principle is inequivalent to but conservative over the Vop\v{e}nka scheme (2016) (0)
L O ] 3 0 Ju l 2 00 3 P 6 = NP ∩ co-NP for Infinite Time Turing Machines (2008) (0)
Makoto Kikuchi SET-THEORETIC MEREOLOGY (2016) (0)
The Sigma_1-definable universal finite sequence (2019) (0)
Weakly Homogeneous Structures (2017) (0)
Infinite Hex is a draw (2022) (0)
Inner models with large cardinal features usually obtained by forcing (2011) (0)
Pseudo-countable models (2022) (0)
Review: Yiannis N. Moschovakis, Notes on Set Theory (1997) (0)
CLASSIFICATION OF RESEARCH (2014) (0)
Symbolic Logic , June , 1998 ] Gap Forcing (1998) (0)
CLASSIFICATION OF RESEARCH (2014) (0)
6 N ov 2 00 2 A class of strong diamond principles (2008) (0)
A ug 1 99 8 Universal Indestructibility (1998) (0)
Modal model theory (2020) (0)
Ju l 2 00 3 A Generalization of the Gap Forcing Theorem (2003) (0)
Fe b 20 06 Degrees of Rigidity for Souslin Trees (2018) (0)
L O ] 3 D ec 2 00 2 Infinite time Turing machines (2022) (0)
CUNY COLLABORATION IN MATHEMATICAL LOGIC ARTHUR W. APTER, BARUCH COLLEGE JOEL D. HAMKINS, COLLEGE OF STATEN ISLAND ROMAN KOSSAK, BRONX COMMUNITY COLLEGE GEORGE LEIBMAN, BRONX COMMUNITY COLLEGE RUSSELL G. MILLER, QUEENS COLLEGE HANS SCHOUTENS, NYC COLLEGE OF TECHNOLOGY (2005) (0)
Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers (2019) (0)
George Tourlakis. Lectures in Logic and Set Theory, volumes 1 and 2. Cambridge studies in advanced mathematics, vol. 83. Cambridge University Press, Cambridge, UK, 2003. xi + 328 and xv + 575 pp. (2005) (0)
Categorical large cardinals and the tension between categoricity and set-theoretic reflection (2020) (0)
Inner-Model Reflection Principles (2019) (0)
E-recursive intuitions (2013) (0)
Choiceless large cardinals and set‐theoretic potentialism (2020) (0)
Strongly uplifting cardinals and the boldface resurrection axioms (2017) (0)
Forcing as a computational process (2020) (0)

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