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

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• 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

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

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• 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

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• 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

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

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

THE STRENGTH OF THE TREE THEOREM FOR PAIRS IN REVERSE MATHEMATICS LUDOVIC PATEY Abstract. No natural principle is currently known to be strictly between the arithmetic comprehension axiom (ACA0 ) and Ramsey’s theorem f

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• Large numbers
• Mathematical notation
• Probability theory
• Differential forms
• Symbol

Devoir maison sur l’´elimination des coupures Ludovic Patey 29 janvier

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Π01 ENCODABILITY AND OMNISCIENT REDUCTIONS BENOIT MONIN AND LUDOVIC PATEY Abstract. A set of integers A is computably encodable if every infinite set of integers has an infinite subset computing A. By a result of Solova

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• Computability theory
• 01 class
• Riemann surfaces
• Probability theory
• Measure theory
• Differential forms on a Riemann surface
• Modulus of continuity

ON THE LOGICAL STRENGTHS OF PARTIAL SOLUTIONS TO MATHEMATICAL PROBLEMS LAURENT BIENVENU, LUDOVIC PATEY, AND PAUL SHAFER ABSTRACT. We use the framework of reverse mathematics to address the question of, given a mathematic

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• Computability theory
• Logic
• Proof theory
• Mathematics
• Mathematical logic
• Reverse mathematics
• Model theory
• Philosophy of mathematics
• Symbol
• Fixed-point theorems
• Primitive recursive functional
• Generalised Whitehead product

Reverse Mathematics and a Weak Ramsey-Type K¨onig’s Lemma Ludovic Patey Laurent Bienvenu

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• Mathematics
• Logic
• Mathematical logic
• Proof theory
• Abstraction
• Computability theory
• Reverse mathematics
• Second-order arithmetic
• Theorem
• Lemma

˝ DOMINATING THE ERDOS-MOSER THEOREM IN REVERSE MATHEMATICS LUDOVIC PATEY Abstract. The Erd˝

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• Mathematical analysis
• Mathematics
• Measure theory
• Computability theory
• Computable function
• Theory of computation
• Probability theory
• Differential forms
• Relationships among probability distributions
• Sigma-algebra