Theodore Slaman | Academic Influence

Theodore Slaman's AcademicInfluence.com Rankings

Theodore Slaman

Mathematics

#3863

World Rank

#5600

Historical Rank

#1386

USA Rank

Measure Theory

#2324

World Rank

#2780

Historical Rank

#654

USA Rank

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Mathematics

Theodore Slaman's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Theodore Slaman Influential?

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According to Wikipedia, Theodore Allen Slaman is a professor of mathematics at the University of California, Berkeley who works in recursion theory. Slaman and W. Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, which conjectures that the partial order of the Turing degrees is logically equivalent to second-order arithmetic. They showed that the Bi-interpretability Conjecture is equivalent to there being no nontrivial automorphism of the Turing degrees. They also exhibited limits on the possible automorphisms of the Turing degrees by showing that any automorphism will be arithmetically definable.

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Theodore Slaman'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

On the strength of Ramsey's theorem for pairs (2001) (218)
Generic Copies of Countable Structures (1989) (153)
Randomness and Recursive Enumerability (2001) (136)
On the Strength of Ramsey's Theorem (1995) (125)
Definable functions on degrees (1988) (87)
Relative to any nonrecursive set (1998) (76)
THE METAMATHEMATICS OF STABLE RAMSEY'S THEOREM FOR PAIRS (2014) (69)
Defining the Turing Jump (1999) (68)
The atomic model theorem and type omitting (2009) (60)
Comparing DNR and WWKL (2004) (58)
Definability in the Turing degrees (1986) (53)
Measures and Their Random Reals (2008) (53)
Extremes in the Degrees of Inferability (1994) (50)
Complementation in the Turing degrees (1989) (45)
Working below a high recursively enumerable degree (1993) (44)
A polynomial-time algorithm for computing absolutely normal numbers (2013) (44)
Computability, enumerability, unsolvability: directions in recursion theory (1996) (42)
When oracles do not help (1991) (42)
Σ2-collection and the infinite injury priority method (1988) (41)
The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs (2014) (38)
Σn-bounding and Δn-induction (2004) (37)
Working below a low2 recursively enumerably degree (1990) (34)
Π11-conservation of combinatorial principles weaker than Ramsey’s theorem for pairs (2012) (32)
On the theory of the PTIME degrees of the recursive sets (1988) (32)
The Density of Infima in the Recursively Enumerable Degrees (1991) (31)
Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations (2011) (29)
Extension of embeddings in the computably enumerable degrees (2001) (28)
Every Set has a Least Jump Enumeration (2000) (27)
Definability in the enumeration degrees (1997) (24)
An almost deep degree (2001) (23)
The Π₃-theory of the computably enumerable Turing degrees is undecidable (1998) (23)
Relatively recursive expansions II (1992) (22)
Σ_{}-bounding and Δ_{}-induction (2004) (21)
Low upper bounds of ideals (2007) (20)
The P-T-degrees of the recursive sets: lattice embeddings, extensions of embeddings and the two quantifier theory (1989) (20)
The inductive strength of Ramsey's Theorem for Pairs (2017) (20)
Relative enumerability in the difference hierarchy (1998) (19)
Corrigendum to: “On the strength of Ramsey's Theorem for pairs” (2009) (19)
On the normality of numbers to different bases (2013) (19)
Relative to any non-Hyperarithmetic Set (2011) (19)
Independence results on the global structure of the Turing degrees (1983) (19)
Definability in the Recursively Enumerable Degrees (1996) (19)
A computable absolutely normal Liouville number (2015) (18)
Completely Mitotic r.e. Degrees (1989) (18)
Algebraic aspects of the computably enumerable degrees. (1995) (17)
A Basis Theorem for Perfect Sets (1998) (17)
Computational prospects of infinity Part II, Presented talks / (2008) (16)
On simply normal numbers to different bases (2013) (16)
GLOBAL PROPERTIES OF THE TURING DEGREES AND THE TURING JUMP (2007) (15)
Some Results on Effective Randomness (2004) (14)
Random reals, the rainbow Ramsey theorem, and arithmetic conservation (2013) (14)
Generics for computable Mathias forcing (2014) (14)
On zeros of Martin-Löf random Brownian motion (2014) (13)
Normal Numbers and the Borel Hierarchy (2013) (13)
Degrees of inferability (1992) (12)
The irrationality exponents of computable numbers (2014) (12)
On the Σ2-theory of the upper semilattice of Turing degrees (1993) (12)
THE COMPLEXITY OF THE INDEX SETS OF א 0-CATEGORICAL THEORIES AND OF EHRENFEUCHT THEORIES (2006) (12)
A splitting theorem for n - REA degrees (2001) (11)
Mathematical Logic and Applications (1989) (11)
Jump embeddings in the Turing degrees (1991) (11)
A limit on relative genericity in the recursively enumerable sets (1989) (11)
Aspects of the Turing Jump (2002) (11)
The Sacks density theorem and Σ2-bounding (1996) (11)
On Extensions of Embeddings into the Enumeration Degrees of the -Sets (2005) (10)
The Π20 enumeration degrees are not dense (1996) (10)
Turing incomparability in Scott sets (2006) (10)
On Turing Reducibility (1994) (9)
Reflection and forcing in E-recursion theory (1985) (9)
Degree Structures (2010) (9)
The Slaman-Wehner theorem in higher recursion theory (2011) (8)
Probability Measures and Effective Randomness (2007) (8)
The complexity of the index sets of $\aleph_0$-categorical theories and of Ehrenfeucht theories (2006) (8)
On the construction of absolutely normal numbers (2017) (8)
E-recursion, forcing and C*-algebras (2014) (7)
The n-R.E. Degrees: Undecidability and σ1 Substructures (2012) (7)
$$\Pi^0_1$$-Presentations of Algebras (2006) (7)
Sigma~n-bounding and Delta~n-induction (2004) (7)
Computably Enumerable Algebras, Their Expansions, and Isomorphisms (2005) (7)
The Atomic Model Theorem (2007) (7)
Effective randomness for continuous measures (2018) (7)
Computational prospects of infinity Part I, Tutorials / (2008) (6)
On a question of Brown and Simpson (1996) (6)
A NOTE ON INITIAL SEGMENTS OF THE ENUMERATION DEGREES (2014) (5)
Lattice initial segments of the turing degrees (2002) (5)
THE STRENGTH OF RAMSEY’S THEOREM FOR PAIRS AND ARBITRARILY MANY COLORS (2017) (5)
On the existence of a strong minimal pair (2015) (5)
∑2 Induction and infinite injury priority arguments, part III: Prompt sets, minimal pairs and Shoenfield’s Conjecture (2001) (5)
K-TRIVIALS ARE NEVER CONTINUOUSLY RANDOM (2011) (5)
Extending Partial Orders to Dense Linear Orders (1998) (4)
Π 01-presentations of algebras ∗ (2005) (4)
Σ1 definitions with parameters (1986) (4)
Recursive in a generic real (2000) (4)
Pi0a Classes and Minimal Degrees (1997) (4)
Forcing, Iterated Ultrapowers, and Turing Degrees (2015) (4)
The Theory of the Metarecursively Enumerable Degrees (2006) (3)
Infinity and truth (2014) (3)
Extensional Properties of Sets of Time Bounded Complexity (Extended Abstract) (1989) (3)
Quasi-minimal enumeration degrees and minimal Turing degrees (1998) (3)
The Global Structure of the Turing Degrees (1999) (3)
University of Nevada, Las Vegas, Las Vegas, Nevada June 1–4, 2002 (2003) (3)
On a question of Sierpiński (1999) (2)
Automorphisms in the PTIME-Turing Degrees of Recursive Sets (1997) (2)
The ∀ ∃ theory of D ( ≤ , ∨ , ′ ) is undecidable (2003) (2)
Fragments of the theory of the enumeration degrees (2021) (2)
Generalized Hyperarithmetic Theory (1990) (2)
Irrationality exponent, Hausdorff dimension and effectivization (2016) (2)
On the Theory of the Polynomial Degrees of the Recursive Sets (1988) (2)
The complexity types of computable sets (1989) (2)
Σ _1^1 in Every Real in a Σ _1^1 Class of Reals Is Σ _1^1 (2017) (2)
Differences between Resource Bounded Degree Structures (2003) (2)
The 02 Enumeration Degrees Are Not (2007) (1)
Some problems and results in the theory of actually computable functions (preliminary abstract) (1989) (1)
University of California, Irvine Irvine, California March 27–30, 2008 (2008) (1)
On co-Simple Isols and Their Intersection Types (1992) (1)
The extended plus-one hypothesis—A relative consistency result (1983) (1)
Decidability of the Natural Numbers with the Almost-All Quantifier (2006) (1)
The Δ⁰₂ Turing degrees: Automorphisms and Definability (2017) (1)
Generating Sets for the Recursively Enumerable Turing Degrees (2005) (0)
Chapter 3: Consequences in Descriptive Set Theory (2014) (0)
6 n-Bounding and 1 n-Induction (2003) (0)
Capacitability for Co-Analytic Sets (2022) (0)
L O ] 3 0 A ug 2 01 8 EFFECTIVE RANDOMNESS FOR CONTINUOUS MEASURES (0)
N T ] 4 O ct 2 01 4 The Irrationality Exponents of Computable Numbers Verónica (2014) (0)
The theory of the α degrees is undecidable (2010) (0)
Chapter 13: Ramsey Theory on Ordinals (2014) (0)
Chapter 6: The S-spaces and the L-spaces (2014) (0)
Chapter 5: Variations on the Souslin Hypothesis (2014) (0)
The Sacks Density Theorem and Sigma2-Bounding (1996) (0)
Relative enumerability in the di erence hierarchy (1998) (0)
Splitting and Density for the Recursive Sets of a Fixed Time Complexity (1992) (0)
ON A QUESTION OF SIERPI NSKI (1999) (0)
Irrationality exponent, Hausdorff dimension and effectivization (2017) (0)
Logic and Mathematics (2010) (0)
Schmerl decompositions in first order arithmetic (2019) (0)
Reflection and the priority method in E-recursion theory (1985) (0)
REVIEWS-Defining the Turing jump (2001) (0)
The continuum hypothesis and the theory of the Kleene degrees (1989) (0)
On absolutely normal numbers and their discrepancy estimate (2017) (0)
On the Kleene degrees of Π11 sets (1986) (0)
On the Kleene Degrees of pi11 Sets (1986) (0)
Computability, Enumerability, Unsolvability: APPENDIX: Questions in Recursion Theory (1996) (0)
IN MEMORIAM: GERALD E. SACKS, 1933–2019 (2022) (0)
Córdoba, Argentina September 20–24, 2004 (2005) (0)
SPONSORED BY THE ASSOCIATION FOR SYMBOLIC LOGIC (2013) (0)
Chapter 4: Consequences in Measure Theory (2014) (0)
Chapter 14: Five Cofinal Types (2014) (0)
Mathematical Deenability (2007) (0)
InlineEquation ID=" IEq4"> EquationSource Format=" TEX"> ImageObject Color=" BlackWhite" FileRef=" 153200613ArticleIEq4. gif" Format=" GIF" Rendition=" HTML" Type=" Linedraw"/>-Presentations of Algebras (2006) (0)
Chapter 17: Reflection Principles (2014) (0)
WHICH BOUNDS NO DIAMOND BASES (2001) (0)
Chapter 9: Coherent and Lipschitz Trees (2014) (0)
Computability, Enumerability, Unsolvability: Preface (1996) (0)
OF THE TURING DEGREES (2016) (0)
Chapter 16: Cardinal Arithmetic and (2014) (0)
On Bounded Time Turing Reducibility on the Recursive Sets (1989) (0)
On the Sigma2-Theory of the Upper Semilattice of Turing Degrees (1993) (0)
Chapter 11: Biorthogonal Systems (2014) (0)
Chapter 15: Five Linear Orderings (2014) (0)
Chapter 8: Ideal Dichotomies (2014) (0)
Sigma1 Definitions with Parameters (1986) (0)
Recursion theoretic papers. Introduction to Part VI (2016) (0)
Chapter 10: Applications to the S-space Problem and the von Neumann Problem (2014) (0)
K-trivials are NCR (2008) (0)
The theory of is undecidable (2016) (0)
On simply normal numbers to different bases (2015) (0)
Chapter 2: Coding Sets by the Real Numbers (2014) (0)
Mathematical Logic and Applications: Proceedings of the Logic Meeting Held in Kyoto, 1987 (1989) (0)
On the relationship between the complexity, the degree, and the extension of a computable set (1990) (0)
2008 Annual Meeting of the Association for Symbolic Logic-University of California, Irvine-Irvine, California-March 27-30, 2008-Abstracts (2008) (0)
Chapter 7: The Side-condition Method (2014) (0)
Irrationality Exponent, Hausdorﬀ Dimension and Eﬀectivization (2016) (0)
Chapter 12: Structure of Compact Spaces (2014) (0)
THE UNIVERSITY OF CHICAGO TOPICS IN RECURSIVELY ENUMERABLE SETS AND DEGREES A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MATHEMATICS BY STEFFEN LEMPP (2014) (0)
Limit computability and constructive measure (0)
2010 european summer meeting of the association for symbolic logic logic colloquium'10 (2011) (0)
Chapter 1: Baire Category Theorem and the Baire Category Numbers (2014) (0)
Relative enumerability in the di erence hierarchyMarat (1996) (0)
P 0 1 \pi^01 -presentations of algebras (2006) (0)

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