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Reverse mathematics
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31	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
32	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 Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2015-08-13 12:44:18 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
33	Computability Theory, Reverse Mathematics, and Ordered Fields Oscar Louis Levin, Ph.D. University of Connecticut, 2009 Add to Reading List Source URL: www.math.uconn.edu Language: English - Date: 2009-04-27 16:38:49 Field theory Computability theory Real algebraic geometry Theory of computation Elementary mathematics Ordered field Computable function Field Archimedean property Function Real number Reverse mathematics
34	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
35	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
36	Reverse Mathematics and Well-ordering Principles: A Pilot Study Bahareh Afshari and Michael Rathjen 1,2 Department of Pure Mathematics University of Leeds Leeds, LS2 9JT, UK Add to Reading List Source URL: www1.maths.leeds.ac.uk Language: English - Date: 2009-02-11 08:48:01
37	˝ DOMINATING THE ERDOS-MOSER THEOREM IN REVERSE MATHEMATICS LUDOVIC PATEY Abstract. The Erd˝ Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2015-05-13 11:24:44 Mathematical analysis Mathematics Measure theory Computability theory Computable function Theory of computation Probability theory Differential forms Relationships among probability distributions Sigma-algebra
38	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
39	I NTRODUCTION P RINCIPLES ADMITTING A UNIVERSAL INSTANCE P RINCIPLES ADMITTING NO UNIVERSAL INSTANCE Add to Reading List Source URL: ludovicpatey.com Language: English - Date: 2014-07-04 08:41:44 Computability theory Mathematical logic Proof theory Reverse mathematics Model theory Axiom of choice
40	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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