Richard Shore | Academic Influence

Richard Shore's AcademicInfluence.com Rankings

Richard Shore

Mathematics

#4115

World Rank

#5916

Historical Rank

#1454

USA Rank

Measure Theory

#2713

World Rank

#3241

Historical Rank

#783

USA Rank

mathematics Degrees

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Mathematics

Richard Shore's Degrees

PhD Mathematics Princeton University
Masters Mathematics Princeton University

Why Is Richard Shore Influential?

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According to Wikipedia, Richard Arnold Shore is a professor of mathematics at Cornell University who works in recursion theory, the partial order of the Turing degrees.Shore settled the Rogers respectively, are not isomorphic.In joint work with Theodore Slaman, Shore showed that the Turing jump.

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Richard Shore'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

Degree spectra and computable dimensions in algebraic structures (2002) (185)
Logic for Applications (1997) (154)
The recursively enumerable α-degrees are dense (1976) (151)
Combinatorial principles weaker than Ramsey's Theorem for pairs (2007) (135)
An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees (1984) (118)
Pseudo-jump operators. II: Transfinite iterations, hierarchies and minimal covers (1984) (106)
Degrees of Categoricity and the Hyperarithmetic Hierarchy (2013) (80)
Computable Models of Theories with Few Models (1997) (76)
Pseudojump operators. I. The r.e. case (1983) (69)
Defining the Turing Jump (1999) (68)
Second order logic and first order theories of reducibility orderings (1980) (64)
In Reviews (2003) (62)
The atomic model theorem and type omitting (2009) (60)
The Theory of the Degrees below 0 (1981) (57)
Splitting an -recursively enumerable set (1975) (55)
Reducibility orderings: Theories, definability and automorphisms☆ (1980) (55)
Then-rea enumeration degrees are dense (1992) (52)
The limits of determinacy in second order arithmetic: consistency and complexity strength (2012) (50)
Computable Isomorphisms, Degree Spectra of Relations, and Scott Families (1998) (49)
Computably categorical structures and expansions by constants (1999) (48)
Working below a high recursively enumerable degree (1993) (44)
The Prospects for Mathematical Logic in the Twenty-First Century (2001) (41)
Splitting properties and jump classes (1981) (39)
Nowhere simple sets and the lattice of recursively enumerable sets (1978) (36)
Reasoning about common knowledge with infinitely many agents (1999) (36)
On the strength of König's duality theorem for infinite bipartite graphs (1992) (35)
On homogeneity and definability in the first-order theory of the Turing degrees (1982) (35)
Working below a low2 recursively enumerably degree (1990) (34)
RECURSIVELY ENUMERABLE SETS AND DEGREES A Study of Computably Generated Sets (Perspectives in Mathematical Logic) (1988) (33)
A non-inversion theorem for the jump operator (1988) (31)
On isolating r.e. and isolated d-r.e. degrees (1996) (31)
On the jump of an -recursively enumerable set (1976) (30)
Models and Computability: Effective Model Theory: The Number of Models and Their Complexity (1999) (28)
Controlling the dependence degree of a recursively enumerable vector space (1978) (28)
Decidability and invariant classes for degree structures (1988) (27)
The elementary theory of the recursively enumerable degrees is not N0-categorical (1984) (27)
Reverse Mathematics: The Playground of Logic (2010) (26)
Computability Theory and Its Applications (2000) (26)
On the strength of Fraïssé’s conjecture (1993) (25)
The homogeneity conjecture. (1979) (24)
Finitely generated codings and the degrees r.e. in a degree (1982) (24)
Highness and Bounding Minimal Pairs (1993) (24)
The theory of the recursively enumerable weak truth-table degrees is undecidable (1992) (23)
On the ∀∃-Sentences of α-Recursion Theory (1978) (23)
Minimal a-degrees (1972) (22)
1 1 relations and paths through O (2004) (22)
Countable Thin Pi01 Classes (1993) (22)
Π11 relations and paths through (2004) (21)
The P-T-degrees of the recursive sets: lattice embeddings, extensions of embeddings and the two quantifier theory (1989) (20)
Initial segments of the degrees of size ℵ1 (1986) (20)
Undecidability and 1-Types in the Recursively Enumerable Degrees (1993) (20)
The Recursively Enumerable Degrees (1999) (20)
Natural Definability in Degree Structures (1999) (20)
Definability in the Recursively Enumerable Degrees (1996) (19)
Embeddings and extensions of embeddings in the r.e. tt and wtt-degrees (1985) (19)
Defining jump classes in the degrees below 0 (1988) (18)
Degree Structures: Local and Global Investigations (2006) (17)
Boolean Algebras, Tarski Invariants, and Index Sets (2006) (17)
Direct and Local Definitions of the Turing jump (2007) (16)
Logical Methods: In Honor of Anil Nerode's Sixtieth Birthday (1994) (16)
r-Maximal major subsets (1978) (16)
Characterizations for computable structures (2000) (16)
Lattice embeddings below a nonlow2 recursively enumerable degree (1996) (15)
Computability theory and its applications : current trends and open problems : proceedings of a 1999 AMS-IMS-SIAM Joint Summer Research Conference, Computability Theory and Applications, June 13-17, 1999, University of Colorado, Boulder (2000) (15)
Degree theoretic definitions of the low2 recursively enumerable sets (1995) (15)
The limits of determinacy in second order arithmetic: consistency and complexity strength (2014) (14)
Domination, forcing, array nonrecursiveness and relative recursive enumerability (2012) (14)
Determining automorphisms of the recursively enumerable sets (1977) (14)
The maximal linear extension theorem in second order arithmetic (2010) (14)
Undecidability and initial segments of the (r.e.) tt-degrees (1990) (13)
A computably categorical structure whose expansion by a constant has infinite computable dimension (2003) (13)
Interpolating d-r.e. and REA Degrees between r.e. Degrees (1996) (12)
Σ n sets which are Δ n -incomparable (uniformly) (1974) (11)
A splitting theorem for n - REA degrees (2001) (11)
α-Recursion Theory (1977) (10)
Invariants, Boolean algebras and ACA$_{0}^{+}$ (2005) (10)
There is no degree invariant half-jump (1997) (10)
Conjectures and questions from Gerald Sacks's Degrees of Unsolvability (1997) (9)
Square bracket partition relations in L (1974) (9)
THE TURING DEGREES: AN INTRODUCTION (2015) (9)
Some More Minimal Pairs of α-Recursively Enumerable Degrees (1978) (9)
Types of simple α-recursively enumerable sets (1976) (9)
Generalized high degrees have the complementation property (2004) (9)
Interpreting True Arithmetic in the Theory of the r.e. Truth Table Degrees (1995) (9)
Topological aspects of the Medvedev lattice (2011) (9)
Computably Enumerable Partial Orders (2011) (8)
Definable degrees and automorphisms of $\mathcal {D}$ (1981) (8)
$\Sigma_n$ Sets which are $\Delta_n$-Incomparable (Uniformly) (1974) (8)
Erratum to "Computable Isomorphisms, Degree Spectra of Relations, and Scott Families" (1999) (8)
Biinterpretability up to double jump in the degrees below 0 (2013) (8)
Splitting Theorems and the Jump Operator (1998) (7)
Abstract State Machines: Designing Distributed Systems with State Machines and B (1998) (7)
The n-R.E. Degrees: Undecidability and σ1 Substructures (2012) (7)
The irregular and non-hyperregular α-r.e. degrees (1975) (7)
The Atomic Model Theorem (2007) (7)
A computably stable structure with no Scott family of finitary formulas (2006) (7)
The Degrees of Constructibility of Cohen Reals (1986) (6)
Rigidity and biinterpretability in the hyperdegrees (2005) (6)
Undecidability and initial segments of the wtt-degrees ≤0′ (1990) (6)
The ∀∃-theory of ℛ(≤,∨,∧) is undecidable (2003) (6)
Jumps of Minimal Degrees Below 0 (1996) (6)
Effective Mathematics of the Uncountable: Reverse mathematics, countable and uncountable: a computational approach (2013) (6)
The degrees of unsolvability: Global results (1981) (5)
The settling-time reducibility ordering (2007) (5)
The lown and lowm r. e. degrees are not elementarily equivalent (2004) (5)
Undecidability and 1-types in intervals of the computably enumerable degrees (2000) (4)
Intervals Without Critical Triples (1995) (4)
Priority arguments in α-recursion theory, (1972) (4)
A direct construction of a minimal recursively enumerable truth-table degree (1990) (4)
Logic for Applications (1993) (4)
The Turing and Truth-Table-Degrees are not Elementarily Equivalent* (1982) (4)
Initial segments of the degrees of constructibility (1988) (4)
Lattice initial segments of the hyperdegrees (2010) (4)
Alonzo Church (1997) (4)
Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem (2017) (4)
Recursive Models of Theories with Few Models (1998) (4)
The Theory of the Metarecursively Enumerable Degrees (2006) (3)
On large cardinals and partition relations (1971) (3)
Solutions of the Goncharov-Millar and Degree Spectra Problems in The Theory of Computable Models (2000) (3)
Logical methods in mathematics and computer science: A symposium in honor of Anil Nerode's sixtieth birthday (1993) (3)
Decomposition and infima in the computably enumerable degrees (2003) (3)
Minimal degrees which are Sigma~2^0 but not Delta~2^0 (2003) (3)
Cohesive sets: countable and uncountable (1974) (3)
Computing maximal chains (2012) (3)
Computable Structures: Presentations Matter (1999) (2)
Σ _1^1 in Every Real in a Σ _1^1 Class of Reals Is Σ _1^1 (2017) (2)
Local Definitions in Degree Structures: The Turing Jump, Hyperdegrees and Beyond (2007) (2)
Almost Theorems of Hyperarithmetic Analysis (2022) (2)
The ∀ ∃ theory of D ( ≤ , ∨ , ′ ) is undecidable (2003) (2)
CONSERVATIVITY OF ULTRAFILTERS OVER SUBSYSTEMS OF SECOND ORDER ARITHMETIC (2018) (2)
Some Constructions in α-Recursion Theory (1980) (2)
Infima of recursively enumerable truth table degrees (1988) (2)
The strength of Turing determinacy within second order arithmetic (2016) (2)
Categoricity and Scott Families (1996) (2)
Jumps of Ʃ02-high e-degrees and properly Ʃ02 e-degrees (1999) (2)
THE TURING DEGREES BELOW GENERICS AND RANDOMS (2014) (1)
A nonlow2 R. E. Degree with the Extension of Embeddings Properties of a low2 Degree (2002) (1)
The theories of the t , tt and wtt r . E . Degrees : undecidability and beyond (1993) (1)
Π₁¹ Relations and Paths through ᵊ (2004) (1)
DEFINABLE DEGREES AND AUTOMORPHISMS OF V BY (2007) (1)
Low Level Nondelegability Results: Domination and Recursive Enumeration (2013) (1)
The complexity of ascendant sequences in locally nilpotent groups (2014) (1)
The strength of the Grätzer-Schmidt theorem (2009) (1)
Mass problems and density (2016) (1)
The Strength of the Gr\"atzer-Schmidt Theorem (2014) (1)
The arithmetic and Turing degrees are not elementarily equivalent (1984) (1)
The strength of the Grätzer-Schmidt theorem (2016) (1)
Weak compactness and square bracket partition relations (1972) (1)
sigman Sets which are trianglen-Incomparable (Uniformly) (1974) (0)
THEOREMS OF HYPERARITHMETIC ANALYSIS AND ALMOST THEOREMS OF HYPERARITHMETIC ANALYSIS (2022) (0)
A few results (2010) (0)
The Bulletin of Symbolic Logic (1995) (0)
JSL volume 49 issue 4 Cover and Back matter and Errata (1984) (0)
On the Jumps of the Degrees Below a Recursively Enumerable Degree (2018) (0)
Annual Meeting of the Association for Symbolic Logic, Los Angeles, 1989 (1990) (0)
1997 european summer meeting of the association for symbolic logic (1998) (0)
Every incomplete computably enumerable truth-table degree is branching (2001) (0)
Undecidability and Beyond (2007) (0)
Series Scott Families and Computably Categorical Structures (1996) (0)
Jumps of Sigma(0)(2)-high e-degrees and properly Sigma(0)(2) e-degrees (1999) (0)
ASSOCIATION FOR SYMBOLIC LOGIC (2018) (0)
Computably Presentable Models of Theories with Few Models (1996) (0)
The Reviews, Bull. Symbolic Logic 9, iss. 1 (2003) (2003) (0)
REVIEWS-Defining the Turing jump (2001) (0)
SEPARATING COMBINATORIAL PRINCIPLES OVER WEAK KÖNIG ’ S LEMMA (2015) (0)
ℒ*() and other lattices of recursively enumerable sets (1980) (0)
On isolating re and isolated dr. e. degrees (1996) (0)
Logic Colloquium '95, Haifa, Israel, 9-17 August 1995 - Preface (1997) (0)
Andersson, A., On second-order generalized quanti" ers and" finite structures (2002) (0)
Degrees of Constructibility (1992) (0)
Archangel&y, DA, Dekhtyar, MI and Taitslin, MA, Linear logic for (1996) (0)
Index of Reviews (1980) (0)
Computing maximal chains (2012) (0)
JSL volume 50 issue 4 Cover and Back matter and Errata (1985) (0)
1995–1996 annual meeting of the association for symbolic logic (1996) (0)
The theory of is undecidable (2016) (0)
Pi11 relations and paths through (2004) (0)
Contemporary Mathematics Natural Definability in Degree Structures (1999) (0)
Downey, R., f, iiForte, G. and Nies, A., Addendum to (1999) (0)
Scott Families and Computably Categorical Structures (1996) (0)
On the jumps of the degrees below an r.e. degree (2015) (0)
Types of Simple alpha-Recursively Enumerable Sets (1976) (0)
Master Index to Volumes 61-70 (1994) (0)
JSL volume 48 issue 3 Cover and Front matter (1983) (0)
Elements of Set Theory (1997) (0)
1994 European Summer Meeting of the Association for Symbolic Logic: Logic Colloquium'94 (1995) (0)

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