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Ramsey theory
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11	BROWN’S LEMMA IN SECOND-ORDER ARITHMETIC EMANUELE FRITTAION Abstract. We show that Brown’s lemma is equivalent to IΣ02 over RCA∗0 . We also show that (the infinite) van der Waerden’s theorem is equivalent to BΣ Add to Reading List Source URL: www.math.tohoku.ac.jp Language: English - Date: 2016-02-20 21:08:30 Mathematics Ergodic theory Ramsey theory Semigroup theory Lemmas Combinatorics Piecewise syndetic set Partition regularity Syndetic set Diagonal lemma IP set BanachAlaoglu theorem
12	Math´ematiques `a rebours et un Lemme de K¨onig Faible de Type Ramsey Stage de Master 2 - MPRI mars - aoˆ ut 2012 Ludovic Patey ∗ Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2013-04-16 05:40:26 Mathematical logic Computability theory Mathematics Theoretical computer science Proof theory Logic in computer science Theory of computation Second-order arithmetic Combinatory logic Reverse mathematics Computable function
13	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 Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2016-05-31 11:43:35 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
14	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 Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2015-10-26 09:24:01 Computability theory Mathematical logic Proof theory Theory of computation Logic in computer science Computable function Reverse mathematics PA degree Peano axioms
15	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 Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2015-01-27 11:28:33 Computability theory Theory of computation Mathematics Theoretical computer science Mathematical analysis Computable function Sigma-algebra Generalised Whitehead product
16	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 Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2015-12-11 11:48:38 Large numbers Mathematical notation Probability theory Differential forms Symbol
17	T HE HIERARCHIES M ATHIAS - LIKE FORCING Controlling iterated jumps of Ramsey-type theorems Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2015-09-20 15:03:06 Computability theory Low
18	U NIVERSITÉ PARIS D IDEROT – PARIS VII S ORBONNE PARIS C ITÉ É COLE D OCTORALE S CIENCES M ATHÉMATIQUES DE PARIS C ENTRE THÈSE en vue d’obtenir le grade de Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2016-02-09 12:07:59 Computability theory Ramsey theory Theorem Graph coloring Reverse mathematics
19	Reverse Mathematics and a Weak Ramsey-Type K¨onig’s Lemma Ludovic Patey Laurent Bienvenu Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2013-04-16 05:41:23 Mathematics Logic Mathematical logic Proof theory Abstraction Computability theory Reverse mathematics Second-order arithmetic Theorem Lemma
20	Fachbereich Mathematik Proof mining and combinatorics Program extraction for Ramsey’s theorem for pairs Vom Fachbereich Mathematik Add to Reading List Source URL: tuprints.ulb.tu-darmstadt.de Language: English - Date: 2012-05-15 05:15:29 Mathematics Topology Mathematical analysis Computability theory General topology Proof theory Mathematical logic Reverse mathematics BolzanoWeierstrass theorem HeineBorel theorem Intermediate value theorem Primitive recursive function

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