A LIGHTFACE ANALYSIS OF THE DIFFERENTIABILITY RANK LINDA BROWN WESTRICK Abstract. We examine the computable part of the differentiability hierarchy defined by Kechris and Woodin. In that hierarchy, the rank of a differen

Source URL: www.math.uconn.edu

• Ordinal numbers
• Proof theory
• Computability theory
• Mathematical notation
• Ordinal notation
• Continuous function
• Constructible universe
• Limit of a function
• Symbol
• NC
• Computable number
• Fast-growing hierarchy

Effective bounds from ineffective proofs in analysis: an application of functional interpretation and majorization∗ Ulrich Kohlenbach Fachbereich Mathematik, J.W.Goethe–Universitt Robert–Mayer–Str. 6–10, 6000 F

Source URL: www.mathematik.tu-darmstadt.de

• Computability theory
• Mathematical logic
• Logic
• Primitive recursive functional
• Proof theory
• Symbol
• Mathematics
• Table of stars with Bayer designations

RAMSEY’S THEOREM FOR SINGLETONS AND STRONG COMPUTABLE REDUCIBILITY DAMIR D. DZHAFAROV, LUDOVIC PATEY, REED SOLOMON, AND LINDA BROWN WESTRICK Abstract. We answer a question posed by Hirschfeldt and Jockusch by showing

Source URL: ludovicpatey.com

• Mathematics
• Mathematical analysis
• Differential forms
• Constructible universe
• Closed and exact differential forms
• Computability theory
• Combinatory logic
• Ordinal number
• Differential forms on a Riemann surface
• Banach fixed-point theorem

On uniform weak K¨onig’s lemma Ulrich Kohlenbach BRICS∗ Department of Computer Science University of Aarhus Ny Munkegade

Source URL: www.mathematik.tu-darmstadt.de

• Computability theory
• Proof theory
• Mathematical logic
• Predicate logic
• Logic in computer science
• Primitive recursive functional
• Reverse mathematics
• Primitive recursive function
• Primitive recursive arithmetic
• First-order logic
• Peano axioms
• Ordinal analysis

OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS LUDOVIC PATEY Abstract. Ramsey’s theorem states that for any coloring of the n-element subsets of N with finitely many colors, there is an infinite set

Source URL: ludovicpatey.com

• Computability theory
• Mathematical logic
• Proof theory
• Theory of computation
• Logic in computer science
• Computable function
• Reverse mathematics
• PA degree
• Peano axioms

THE WEAKNESS OF BEING COHESIVE, THIN OR FREE IN REVERSE MATHEMATICS LUDOVIC PATEY Abstract. Informally, a mathematical statement is robust if its strength is left unchanged under variations of the statement. In this pape

Source URL: ludovicpatey.com

• Computability theory
• Computable function
• Computation in the limit
• Second-order arithmetic
• Compactness theorem
• Reverse mathematics
• 01 class
• PA degree
• Low
• Algorithmically random sequence
• Computable number

Things that can and things that can’t be done in PRA Ulrich Kohlenbach BRICS∗ Department of Computer Science University of Aarhus Ny Munkegade, Bldg. 540

Source URL: www.mathematik.tu-darmstadt.de

• Computability theory
• Mathematical logic
• Mathematics
• Theoretical computer science
• Primitive recursive function
• Primitive recursive arithmetic
• ELEMENTARY
• Reverse mathematics
• Pairing function
• Ackermann function
• Sequence
• Recursion

ON THE COMPUTABILITY OF CONDITIONAL PROBABILITY NATHANAEL L. ACKERMAN, CAMERON E. FREER, AND DANIEL M. ROY Abstract. As inductive inference and machine learning methods in computer science see continued success, research

Source URL: danroy.org

Towards a Theory of Peer-to-Peer Computability Joachim Giesen Roger Wattenhofer Aaron Zollinger {giesen,wattenhofer,zollinger}@inf.ethz.ch Department of Computer Science, ETH Zurich, 8092 Zurich, Switzerland

Source URL: disco.ethz.ch

• Graph theory
• Complex systems theory
• Graph
• Directed acyclic graph
• Peer-to-peer
• Tree
• Social peer-to-peer processes
• Consensus

Ramsey-type graph coloring and diagonal non-computability Ludovic Patey Abstract A function is diagonally non-computable (d.n.c.) if it diagonalizes against the universal partial computable function. D.n.c. functions pla

Source URL: ludovicpatey.com

• Computability theory
• Theory of computation
• Mathematics
• Theoretical computer science
• Mathematical analysis
• Computable function
• Sigma-algebra
• Generalised Whitehead product