R

R

• in: Freund A. and Kohlenbach U.
  "R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces" (2022)
• in: Kohlenbach U.
  "On quantitative versions of theorems due to F.E. Browder and R. Wittmann" (2011)
• in: Leuştean L.
  "Proof mining in $R$-trees and hyperbolic spaces " (2006)

Ramsey

• in: Kreuzer A.P. and Kohlenbach U.
  "Term extraction and Ramsey's theorem for pairs." (2012)
• in: Kreuzer A.P. and Kohlenbach U.
  "Ramsey's theorem for pairs and provably recursive functions" (2009)

Rate

• in: Briseid E.M.
  "A Rate of Convergence for Asymptotic Contractions" (2007)
• in: Freund A. and Kohlenbach U.
  "R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces" (2022)
• in: Körnlein D. and Kohlenbach U.
  "Rate of metastability for Bruck's iteration of pseudocontractive mappings in Hilbert space" (2014)
• in: Kohlenbach U.
  "A polynomial rate of asymptotic regularity for compositions of projections in Hilbert space" (2019)
• in: Kohlenbach U.
  "Mathematically strong subystems of analysis with low rate of growth of provably recursive functionals" (1996)
• in: Leuştean L.
  "A quadratic rate of asymptotic regularity in CAT(0)-spaces" (2007)
• in: Pinto P.
  "A rate of metastability for the Halpern type Proximal Point Algorithm" (2021)

Rates

• in: Briseid E.M.
  "Logical Aspects of Rates of Convergence in Metric Spaces" (2009)
• in: Findling R. and Kohlenbach U.
  "Rates of convergence and metastability for Chidume's algorithm for the approximation of zeros of accretive operators in Banach spaces" (2024)
• in: Kohlenbach U. and Powell T.
  "Rates of convergence for iterative solutions of equations involving set-valued accretive operators" (2020)
• in: Kohlenbach U., López-Acedo G. and Nicolae A.
  "Moduli of regularity and rates of convergence for Fejér monotone sequences" (2019)
• in: Koutsoukou-Argyraki A. and Kohlenbach U.
  "Rates of convergence and metastability for abstract Cauchy problems generated by accretive operators" (2015)
• in: Leuştean L. and Pinto P.
  "Rates of asymptotic regularity for the alternating Halpern-Mann iteration" (2024)
• in: Leuştean L.
  "Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings" (2007)
• in: Pischke N. and Kohlenbach U.
  "Effective rates for iterations involving Bregman strongly nonexpansive operators" (2024)
• in: Pischke N.
  "Rates of convergence for the asymptotic behavior of second-order Cauchy problems" (2024)
• in: Treusch J. and Kohlenbach U.
  "Rates of convergence for splitting algorithms" (2025)

Rathjen M.

• in: Aguilera J.P., Freund A., Rathjen M. and Weiermann A.
  "Boundedness theorems for flowers and sharps" (2022)
• in: Aguilera J.P., Freund A., Rathjen M. and Weiermann A.
  "Ackermann and Goodstein go functorial" (2021)
• in: Freund A., Rathjen M. and Weiermann A.
  "Minimal bad sequences are necessary for a uniform Kruskal theorem" (2022)
• in: Freund A. and Rathjen M.
  "Derivatives of normal functions in reverse mathematics" (2021)

Real

• in: Ambos-Spies K., Brandt U. and Ziegler M.
  "Real Benefit of Promises and Advice" (2013)
• in: Escardó M. and Streicher T.
  "Induction and recursion on the partial real line with applications to Real PCF." (1999)
• in: Gärtner T. and Ziegler M.
  "Real Analytic Machines and Degrees" (2011)
• in: Herrmann C., Sokoli J. and Ziegler M.
  "Satisfiability of cross product terms is complete for real nondeterministic polytime Blum-Shub-Smale machines" (2013)
• in: Ziegler M.
  "Real Computation with Least Discrete Advice" (2012)

Realisability

in: Marz M., Rohr A. and Streicher T.
"Full abstraction and universality via realisability" (1999) 

Realizability

• in: Escardó M. and Streicher T.
  "In domain realizability, not all functionals on $C[-1,1]$ are continuous." (2002)
• in: Hofmann M., Oosten (van) J. and Streicher T.
  "Well-foundedness in realizability" (2006)
• in: Lietz P. and Streicher T.
  "Realizability models refuting Ishihara's boundedness principle." (2012)
• in: Maschio S. and Streicher T.
  "Models of intuitionistic set theory in subtoposes of nested realizability toposes" (2015)
• in: Oliva P. and Streicher T.
  "On Krivine's realizability interpretation of classical second-order arithmetic" (2008)
• in: Streicher T.
  "A classical realizability model arising from a stable model of untyped lambda calculus." (2017)
• in: Streicher T.
  "Krivine's Classical Realizability from a Categorical Perspective" (2013)

Realizations

in: Kohlenbach U.
"Remarks on Herbrand normal forms and Herbrand Realizations" (1992) 

Real-number

in: Escardó M., Hofmann M. and Streicher T.
"On the non-sequential nature of the interval-domain model of real-number computation" (2004) 

Recent

in: Kohlenbach U.
"Recent progress in proof mining in nonlinear analysis" (2017) 

Recognizability

in: Blumensath A. and Courcelle B.
"Recognizability, Hypergraph Operations, and Logical Types" (2006) 

Reconstruction

in: Altenkirch T., Hofmann M. and Streicher T.
"Categorical reconstruction of a reduction free normalization proof." (1995) 

Recovery

in: Khan M.A.A. and Kohlenbach U.
"Quantitative image recovery theorems" (2014) 

Recursion

• in: Escardó M. and Streicher T.
  "Induction and recursion on the partial real line with applications to Real PCF." (1999)
• in: Freund A.
  "What is effective transfinite recursion in reverse mathematics?" (2020)
• in: Kreuzer A.P.
  "Primitive recursion and the chain antichain principle." (2012)
• in: Otto M.
  "Eliminating recursion in the mu-calculus" (1999)

Recursive

• in: Kohlenbach U.
  "Mathematically strong subystems of analysis with low rate of growth of provably recursive functionals" (1996)
• in: Kreuzer A.P. and Kohlenbach U.
  "Ramsey's theorem for pairs and provably recursive functions" (2009)
• in: Streicher T.
  "A universality theorem for PCF with recursive types, parallel-or and $\exists$. " (1994)

Reduction

• in: Altenkirch T., Hofmann M. and Streicher T.
  "Categorical reconstruction of a reduction free normalization proof." (1995)
• in: Otto M.
  "A reduction scheme for phase spaces with almost-Kähler symmetry - regularity results for momentum level sets" (1987)

Reduction-free

in: Altenkirch T., Hofmann M. and Streicher T.
"Reduction-free normalisation for a polymorphic system" (1996) 

Refined

in: Gerhardy P.
"Refined Complexity Analysis of Cut Elimination" (2003) 

Reflection

in: Freund A.
"Set-theoretic reflection is equivalent to induction over well-founded classes" (2020) 

Reflections

in: Kohlenbach U.
"Foundational and mathematical uses of higher types" (2002) 

Regularity

• in: Freund A. and Kohlenbach U.
  "R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces" (2022)
• in: Kohlenbach U.
  "A polynomial rate of asymptotic regularity for compositions of projections in Hilbert space" (2019)
• in: Kohlenbach U., López-Acedo G. and Nicolae A.
  "Moduli of regularity and rates of convergence for Fejér monotone sequences" (2019)
• in: Kohlenbach U.
  "On the reverse mathematics and Weihrauch complexity of moduli of regularity and uniqueness" (2019)
• in: Kohlenbach U., López-Acedo G. and Nicolae A.
  "Quantitative asymptotic regularity for the composition of two mappings" (2017)
• in: Kohlenbach U.
  "Uniform asymptotic regularity for Mann iterates" (2003)
• in: Koutsoukou-Argyraki A. and Kohlenbach U.
  "Effective asymptotic regularity for one-parameter nonexpansive semigroups" (2016)
• in: Leuştean L. and Pinto P.
  "Rates of asymptotic regularity for the alternating Halpern-Mann iteration" (2024)
• in: Leuştean L.
  "A quadratic rate of asymptotic regularity in CAT(0)-spaces" (2007)
• in: Leuştean L.
  "Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings" (2007)
• in: Otto M.
  "A reduction scheme for phase spaces with almost-Kähler symmetry - regularity results for momentum level sets" (1987)

Regularization

in: Dinis B. and Pinto P.
"On the convergence of algorithms with Tikhonov regularization terms" (2021) 

Related

• in: Akama Y., Berardi S., Hayashi S. and Kohlenbach U.
  "An arithmetical hierarchy of the law of excluded middle and related principles" (2004)
• in: Fujiwara M. and Kohlenbach U.
  "Interrelation between weak fragments of double negation shift and related principles" (2018)
• in: Kohlenbach U.
  "Local formalizations in nonlinear analysis and related areas and proof-theoretic tameness" (2020)

Relation

in: Erker T., Escardó M. and Keimel K.
"The way-below relation of function spaces over semantic domains" (1998) 

Relations

in: Pauly A. and Ziegler M.
"Relative Computability and Uniform Continuity of Relations" (2013) 

Relative

• in: Kohlenbach U.
  "Relative constructivity" (1998)
• in: Pauly A. and Ziegler M.
  "Relative Computability and Uniform Continuity of Relations" (2013)
• in: Reus B. and Streicher T.
  "Relative completeness for logics of functional programs." (2011)

Remarks

in: Kohlenbach U.
"Remarks on Herbrand normal forms and Herbrand Realizations" (1992) 

Repletion

in: Streicher T.
"Inductive construction of repletion" (1999) 

Report

in: Gerhardy P. and Kohlenbach U.
"General Logical Metatheorems for Functional Analysis" (2005) 

Representation-invariant

in: Otto M.
"The logic of explicitly representation-invariant circuits" (1997) 

Representations

• in: Di Nola A. and Leuştean L.
  "Compact representations of BL-algebras" (2003)
• in: Keimel K.
  "Sheaf Representations of algebraic systems. A personal historical account" (2013)
• in: Leuştean L.
  "Sheaf representations of BL-algebras" (2005)
• in: Leuştean L.
  "Representations of many-valued algebras" (2004)

Research

• in: Gerhardy P. and Kohlenbach U.
  "General Logical Metatheorems for Functional Analysis" (2005)
• in: Leuştean L. and Roşu G.
  "Certifying Kalman Filters" (2003)
• in: Leuştean L. and Roşu G.
  "Certifying Kalman Filters" (2003)

Resemblance

in: Freund A.
"Patterns of resemblance and Bachmann-Howard fixed points" (2022) 

Residuated

in: Wille A.M.
"A Gentzen system for involutive residuated lattices" (2005) 

Resolvents

in: Dinis B. and Pinto P.
"Effective metastability for a method of alternating resolvents" (2024) 

Resource

in: Broy M. and Streicher T.
"Specification and design of shared resource arbitration." (1991) 

Restricted

• in: Kohlenbach U.
  "Intuitionistic choice and restricted classical logic" (2001)
• in: Kohlenbach U.
  "On the arithmetical content of restricted forms of comprehension, choice and general uniform boundedness" (1998)

Results

• in: Blumensath A., Otto M. and Weyer M.
  "Decidability results for the boundedness problem" (2014)
• in: Briseid E.M.
  "Addendum to the Paper: Some Results on Kirk's Asymptotic Contractions" (2007)
• in: Briseid E.M.
  "Some Results on Kirk's Asymptotic Contractions" (2007)
• in: Dinis B. and Pinto P.
  "Quantitative Results on the Multi-Parameters Proximal Point Algorithm" (2021)
• in: Grädel E., Otto M. and Rosen E.
  "Undecidability results for two-variable logics" (1999)
• in: Kohlenbach U.
  "Quantitative results on the Proximal Point Algorithm in uniformly convex Banach spaces" (2021)
• in: Kohlenbach U., Leuştean L. and Nicolae A.
  "Quantitative results on Fejér monotone sequences " (2018)
• in: Löw T. and Streicher T.
  "Universality Results for Models in Locally Boolean Domains" (2006)
• in: Leuştean L. and Pinto P.
  "Quantitative results on a Halpern-type proximal point algorithm" (2021)
• in: Otto M.
  "A reduction scheme for phase spaces with almost-Kähler symmetry - regularity results for momentum level sets" (1987)
• in: Pischke N.
  "Quantitative Results on Algorithms for Zeros of Differences of Monotone Operators in Hilbert Space" (2023)
• in: Streicher T.
  "Dependence and independence results for (impredicative) calculi of dependent types." (1992)
• in: Streicher T.
  "Independence results for calculi of dependent types." (1989)

Reticulation

in: Leuştean L.
"The prime and maximal spectra and the reticulation of BL-algebras" (2003) 

Retractions

in: Kohlenbach U. and Sipoş A.
"The finitary content of sunny nonexpansive retractions" (2021) 

Reus B.

• in: Reus B. and Streicher T.
  "A synthetic theory of sequential domains." (2012)
• in: Reus B. and Streicher T.
  "Relative completeness for logics of functional programs." (2011)
• in: Reus B. and Streicher T.
  "About Hoare logics for higher-order store" (2005)
• in: Reus B. and Streicher T.
  "Semantics and logic of object calculi" (2004)
• in: Reus B. and Streicher T.
  "General synthetic domain theory---a logical approach." (1999)
• in: Reus B. and Streicher T.
  "Classical logic, continuation semantics and abstract machines" (1998)
• in: Reus B. and Streicher T.
  "General synthetic domain theory---a logical approach (extended abstract)" (1997)

Reverse

• in: Freund A. and Rathjen M.
  "Derivatives of normal functions in reverse mathematics" (2021)
• in: Freund A.
  "What is effective transfinite recursion in reverse mathematics?" (2020)
• in: Kohlenbach U.
  "On the reverse mathematics and Weihrauch complexity of moduli of regularity and uniqueness" (2019)
• in: Kohlenbach U.
  "Higher order reverse mathematics" (2005)
• in: Kohlenbach U.
  "Higher order reverse mathematics" (2005)
• in: Kreuzer A.P.
  "Non-principal ultrafilters, program extraction and higher order reverse mathematics." (2012)

Review

in: Freund A.
"A mathematical commitment without computational strength" (2022) 

Revisited

• in: Kohlenbach U. and Pinto P.
  "Fejér monotone sequences revisited" (2025)
• in: Streicher T.
  "Denotational completness revisited" (1999)

Revista

in: Pribeanu C. and Leuştean L.
"Consistence evaluation of a man-machine interaction language using connectionist models" (2000) 

RIACS

in: Leuştean L. and Roşu G.
"Certifying Kalman Filters" (2003) 

Rings

in: Keimel K.
"Some trends in lattice-ordered groups and rings" (1995) 

Rohr A.

in: Marz M., Rohr A. and Streicher T.
"Full abstraction and universality via realisability" (1999) 

Role

• in: Gerhardy P.
  "The Role of Quantifier Alternations in Cut Elimination" (2005)
• in: Kohlenbach U., López-Acedo G. and Nicolae A.
  "A uniform betweenness property in metric spaces and its role in the quantitative analysis of the Lion-Man game" (2021)

Român&

in: Pribeanu C. and Leuştean L.
"Consistence evaluation of a man-machine interaction language using connectionist models" (2000) 

Romania

in: Barbălată C. and Leuştean L.
"Applications of feed-forward neural networks to ecological phenomena forecasting" (2000) 

Rosen E.

in: Grädel E., Otto M. and Rosen E.
"Undecidability results for two-variable logics" (1999) 

Rosenbusch A.P.

• in: Keimel K., Rosenbusch A.P. and Streicher T.
  "Relating Direct and Predicate Transformer Partial Correctness Semantics for a Probabilistic-Nondeterministic Language" (2011)
• in: Keimel K., Rosenbusch A.P. and Streicher T.
  "A Minkowksi Type Duality Mediating Between State and Predicate Transformer Semantics for a Probabilistic Nondeterministic Language" (2009)

Rösnick C.

• in: Kawamura A., Ota H., Rösnick C. and Ziegler M.
  "Computational Complexity of Smooth Differential Equations" (2014)
• in: Kawamura A., Ota H., Rösnick C. and Ziegler M.
  "Computational Complexity of Smooth Differential Equations" (2012)

Roşu G.

• in: Leuştean L. and Roşu G.
  "Certifying Kalman Filters" (2003)
• in: Roşu G., Prasad Venkatesan R., Whittle J. and Leuştean L.
  "Certifying optimality of state estimation programs" (2003)

Roth W.

• in: Fedel M., Keimel K., Montagna F. and Roth W.
  "Imprecise probabilities, bets, and functional analytic methods in Lukasiewicz logic" (2013)
• in: Keimel K. and Roth W.
  "Ordered Cones and Approximation" (1992)

Roy M.F.

in: Kohlenbach U. and Leuştean L.
"Approximate fixed points of nonexpansive functions in product spaces" (2006) 

Royal

• in: Kohlenbach U. and Pischke N.
  "Proof theory and nonsmooth analysis" (2023)
• in: Kohlenbach U. and Leuştean L.
  "On the computational content of convergence proofs via Banach limitd." (2012)

Rprop

in: Leuştean L.
"Liquid flow time series prediction using feed-forward neural networks and Rprop learning algorithm" (2001) 

Rule

• in: Kohlenbach U.
  "A note on Spector's quantifier-free rule of extensionality" (2001)
• in: Kohlenbach U.
  "A note on the $\Pi$₂-induction rule" (1995)

Russian

in: Keimel K.
"Abstract ordered compact convex sets and the algebras of the (sub-)probabilistic powerdomain monad over ordered compact spaces (in Russian)" (2009) 

Rutter I.

in: Bae S.W., Baffier J.F., Chun J., Eades P., Eickmeyer K., Grilli L., Hong S.H., Korman M., Montecchiani F., Rutter I. and Tóth C.D.
"Gap-planar graphs" (2018) 

RWTH

• in: Blumensath A.
  "Structures of Bounded Partition Width" (2003)
• in: Blumensath A.
  "Prefix-Recognisable Graphs and Monadic Second-Order Logic" (2001)
• in: Blumensath A.
  "Automatic Structures" (1999)

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