Gerald Sacks | Academic Influence

Gerald Sacks's AcademicInfluence.com Rankings

Gerald Sacks

Philosophy

#1580

World Rank

#2841

Historical Rank

#626

USA Rank

Logic

#501

World Rank

#924

Historical Rank

#200

USA Rank

philosophy Degrees

Gerald Sacks

Mathematics

#1832

World Rank

#2921

Historical Rank

#741

USA Rank

Set Theory

#18

World Rank

#26

Historical Rank

#9

USA Rank

mathematics Degrees

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Philosophy
Mathematics

Gerald Sacks's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics University of Chicago

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Why Is Gerald Sacks Influential?

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According to Wikipedia, Gerald Enoch Sacks was a logician whose most important contributions were in recursion theory. Named after him is Sacks forcing, a forcing notion based on perfect sets and the Sacks Density Theorem, which asserts that the partial order of the recursively enumerable Turing degrees is dense. Sacks had a joint appointment as a professor at the Massachusetts Institute of Technology and at Harvard University starting in 1972 and became emeritus at M.I.T. in 2006 and at Harvard in 2012.

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Gerald Sacks'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

Higher recursion theory (1990) (441)
A DECISION METHOD FOR ELEMENTARY ALGEBRA AND GEOMETRY (2003) (293)
Saturated Model Theory (1972) (280)
ON THE DEGREES LESS THAN 0 (1963) (166)
Degrees of unsolvability (1965) (129)
The Recursively Enumerable Degrees are Dense (1964) (112)
Countable admissible ordinals and hyperdegrees (1976) (100)
Recursive enumerability and the jump operator (1963) (83)
The α-finite injury method (1972) (79)
Multiple error correction by means of parity checks (1958) (65)
FORCING WITH PERFECT CLOSED SETS (1999) (62)
POST'S PROBLEM, ADMISSIBLE ORDINALS, AND REGULARITY (1966) (59)
A minimal degree less than 0 (1961) (58)
Measure-theoretic uniformity in recursion theory and set theory (1969) (55)
Recursion Theory Week (1985) (38)
Metarecursive sets (1965) (36)
Some minimal pairs of α-recursively enumerable degrees (1972) (29)
The 1-Section of a Type n Object (1974) (25)
A minimal hyperdegree (1967) (22)
The K-Section of a Type n Object (1977) (21)
ON A THEOREM OF LACHLAN AND MARTIN (1967) (19)
A maximal set which is not complete. (1964) (19)
The differential closure of a differential field (1972) (18)
Inadmissible recursion theory (1977) (17)
Bounds on Weak Scattering (2007) (16)
ω-Stable Theories (2009) (15)
Metarecursively enumerable sets and admissible ordinals (1966) (13)
On the Number of Countable Models (1983) (12)
On Suborderings of Degrees of Recursive Unsolvability (1961) (11)
Measure-Theoretic Uniformity (1967) (9)
Atomic models higher up (2008) (9)
Some open questions in recursion theory (1985) (9)
Post's Problem, Absoluteness and Recursion in Finite Types (1980) (8)
Uncountable Gandy Ordinals (1976) (8)
Re Sets Higher up (1977) (7)
Mathematical Logic in the 20th Century (2003) (6)
A simple set which is not effectively simple (1964) (6)
On the reducibility of ⊓11 sets☆ (1971) (5)
Effective bounds on Morley rank (1979) (5)
Remarks against foundational activity (1975) (4)
Recursion Theory: its Generalisations and Applications: Three Aspects of Recursive Enumerability in Higher Types (1980) (3)
Review: A. H. Lachlan, The Impossibility of Finding Relative Complements for Recursively Enumerable Degrees (1971) (3)
RECURSION IN OBJECTS OF FINITE TYPE (1999) (2)
Post's Problem in E-Recursion (1999) (2)
The limits of E-recursive enumerability (1986) (2)
Inverting the half-jump (1983) (2)
Generalized Hyperarithmetic Theory (1990) (2)
Model Theory and Applications (2010) (2)
Constructive Ordinals and Π11 Sets (1990) (2)
ON THE NON-ENUMERABILITY OF L (2016) (2)
Meeting of the Association for Symbolic Logic, New York, 1975 (1977) (1)
E-recursion (1999) (1)
Improving a Bounding Result for Weakly-Scattered Theories (2006) (1)
Correction to On the Degrees Less Than 0 (1963) (1)
Selected logic papers (1999) (1)
The Cantor—Bendixson Derivative (2009) (1)
Effective Forcing versus Proper Forcing (1996) (1)
Elimination of Quantifiers for Real Closed Fields (2009) (0)
Light on a Clouded Hypothesis: Set Theory and the Continuum Hypothesis . Paul J. Cohen. Benjamin, New York, 1966. 160 pp., illus. Cloth, $8; paper, $3.95. (1967) (0)
NOTICES (2019) (0)
Some Other Reading (2009) (0)
Review: J. R. Shoenfield, On Degrees of Unsolvability; J. R. Shoenfield, An Uncountable Set of Incomparable Degrees (1964) (0)
Bounds on the Ranks of 1-Types (2009) (0)
Monomorphisms and Substructures (2009) (0)
Review: Richard M. Friedberg, Hartley Rogers, Reducibility and Completeness for Sets of Integers (1960) (0)
7. An Interpolation Theorem for Recursively Enumerable Degrees (1964) (0)
Chapter XII: Selection and $k$-Sections (1990) (0)
Preface to the Serie (2016) (0)
Hyperregularity and Priority (1990) (0)
5. An Existence Theorem For Recursively Enumerable Degrees (1964) (0)
Skolemization of Structures (2009) (0)
Vaught's Two-Cardinal Theorem (2009) (0)
Measure and Forcing (1990) (0)
Chapter I: Constructive Ordinals and $\Pi^1_1$ Sets (1990) (0)
Σ11 Predicates of Reals (1990) (0)
11. Initial Segments of Degrees (1964) (0)
Chapter XIII: $E$-Recursively Enumerable Degrees (1990) (0)
Priority Arguments in Higher Recursion Theory (2010) (0)
Categoricity in Some Uncountable Power (2009) (0)
Selection and k-Sections (1990) (0)
The Baldwin—Lachlan Theorem (2009) (0)
Chapter VIII: Priority Arguments (1990) (0)
Recursion Theory Week: Proceedings of a Conference Held in Oberwolfach, Frg, March 19-25, 1989 (1990) (0)
Shelah's Uniqueness Theorem (2009) (0)
Keisler's Two-Cardinal Theorem (2009) (0)
E-Recursively Enumerable Degrees (1990) (0)
8. Minimal Upper Bounds for Sequences of Degrees (1964) (0)
Chang's Two-Cardinal Theorem (2009) (0)
Preface - Special Volume Dedicated to the late Stephen Cole Kleene (1996) (0)
Towards Morley's Analysis of l-Types (2009) (0)
Minimal Generators and ω1-Categoricity (2009) (0)
Countability Proviso with Exceptions (2009) (0)
Model Completeness of Algebraically Closed Fields (2009) (0)
Chapter XI: Forcing Computations to Converge (1990) (0)
Prime Model Extensions (2009) (0)
Constructive Ordinals and Sets (2016) (0)
The Fundamental Existence Theorem (2009) (0)
12. Further Results and Conjectures (1964) (0)
Set Theory and the Continuum Hypothesis. Paul J. Cohen. Benjamin, New York, 1966. 160 pp., illus. Cloth, $8; paper, $3.95 (1967) (0)
Differential Fields of Characteristic 0 (2009) (0)
Ordinals and Diagrams (2009) (0)
Predicates of Reals (2016) (0)
MODELS OF LONG SENTENCES I (2011) (0)
Review: Shih-Chao Liu, On Many-One Degrees (1966) (0)
Models and Computability: Recursion Theoretic Memories 1954–1978 (1999) (0)
Meeting of the Association for Symbolic Logic, Washington, D.C. 1975 (1976) (0)
E-recursive intuitions (2013) (0)
3. Uncountable Suborderings of Degrees (1964) (0)
4. The Priority Method Of Friedberg and Muchnik (1964) (0)
Recursion theory week : proceedings of a conference held in Oberwolfach, West Germany, April 15-21, 1984 (1984) (0)
Splitting, Density and Beyond (1990) (0)
ON Lω2,ω MODELS OF SIZE ω2 (2019) (0)
§10. Measure-Theoretic, Category and Descriptive Set-Theoretic Arguments (1964) (0)
Admissibility and Regularity (1990) (0)
JSL volume 32 issue 1 Cover and Front matter (1967) (0)
E-RECURSION 2012 (2014) (0)
The Hyperarithmetic Hierarchy (1990) (0)
The Morley Derivative (2009) (0)
6 . The Jump Operator (1964) (0)
Chapter III: $\Sigma^1_1$ Predicates of Reals (1990) (0)
Preface to revised edition (1964) (0)
Chapter IV: Measure and Forcing (1990) (0)
Direct Systems of Structures (2009) (0)
Preface to the Series Perspectives in Mathematical Logic (2016) (0)
Logical Foundations of Computer Science (2013) (0)
Categories and Functors (2009) (0)
Inverse Systems of Compact Hausdorff Spaces (2009) (0)
SPONSORED BY THE ASSOCIATION FOR SYMBOLIC LOGIC (2013) (0)
Chapter II: The Hyperarithmetic Hierarchy (1990) (0)
Omitting a Type (2009) (0)
E-Closed Structures (1990) (0)
Lachlan A. H.. The impossibility of finding relative complements for recursively enumerable degrees. The journal of symbolic logic, vol. 31 (1966), pp. 434–454. (1971) (0)
Review: J. R. Shoenfield, J. W. Addison, Leon Henkin, Alfred Tarski, Applications of Model Theory to Degrees of Unsolvability (1972) (0)
Shoenfield J. R.. On degrees of unsolvability. Annals of mathematics , second series, vol. 69 (1959), pp. 644–653. Shoenfield J. R.. An uncountable set of incomparable degrees. Proceedings of the American Mathematical Society , vol. 11 (1960), pp. 61–62. (1964) (0)
Review: R. M. Friedberg, The Fine Structure of Degrees of Unsolvability of Recursively Enumerable Sets (1963) (0)
JSL volume 32 issue 2 Cover and Front matter (1967) (0)
Review: Ann H. Ihrig, The Post-Lineal Theorems for Arbitrary Recursively Enumerable Degrees of Unsolvability (1967) (0)
The Differential Closure (2009) (0)
IN MEMORIAM: GERALD E. SACKS, 1933–2019 (2022) (0)
9. Minimal Degrees (1964) (0)
First Order Languages (2009) (0)
Indiscernibles and ω-Stability (2009) (0)
Similarity Types of Structures (2009) (0)
Prime Extensions of Wellordered Chains (2009) (0)
Chapter X: $E$-Closed Structures (1990) (0)
Friedberg Richard M. and Rogers Hartley Jr., Reducibility and completeness for sets of integers. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 5 (1959), pp. 117–125. (1960) (0)
Forcing Computations to Converge (1990) (0)
2 . A Continuum of Mutually Incomparable Degrees (1964) (0)
Chapter IX: Splitting, Density and Beyond (1990) (0)

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