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Ramsey's theorem
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1	TERM EXTRACTION AND RAMSEY’S THEOREM FOR PAIRS ALEXANDER P. KREUZER AND ULRICH KOHLENBACH Abstract. In this paper we study with proof-theoretic methods the function(al)s provably recursive relative to Ramsey’s theore Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2013-09-25 08:51:12 Proof theory Computability theory Logic in computer science Mathematical logic Intuitionism Primitive recursive functional Dialectica interpretation Peano axioms Second-order arithmetic Reverse mathematics Combinatory logic Primitive recursive arithmetic
2	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
3	COLORING THE RATIONALS IN REVERSE MATHEMATICS EMANUELE FRITTAION AND LUDOVIC PATEY Abstract. Ramsey’s theorem for pairs asserts that every 2-coloring of the pairs of integers has an infinite monochromatic subset. In th Add to Reading List Source URL: www.math.tohoku.ac.jp Language: English - Date: 2016-02-20 21:08:40 Logic in computer science Differential forms Combinatory logic Lambda calculus Peano axioms Closed and exact differential forms Banach fixed-point theorem Peetre theorem
4	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
5	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
6	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
7	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
8	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
9	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
10	COLORING THE RATIONALS IN REVERSE MATHEMATICS EMANUELE FRITTAION AND LUDOVIC PATEY Abstract. Ramsey’s theorem for pairs asserts that every 2-coloring of the pairs of integers has an infinite monochromatic subset. In th Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2015-08-07 15:59:27 Mathematics Mathematical analysis Logic in computer science Differential forms Combinatory logic Lambda calculus Peano axioms Closed and exact differential forms Differential forms on a Riemann surface Banach fixed-point theorem

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