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Peano axioms
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1	And the Winners Are... An Axiomatic Approach to Selection from a Set Add to Reading List Source URL: ftp.iza.org Language: English - Date: 2014-07-30 08:59:45 Z notation Axiom S Combination Foundations of mathematics Metric Axiom of infinity Peano axioms
2	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
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	PROOF MINING: A SYSTEMATIC WAY OF ANALYSING PROOFS IN MATHEMATICS ULRICH KOHLENBACH AND PAULO OLIVA Abstract. We call proof mining the process of logically analyzing proofs in mathematics with the aim of obtaining new i Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2012-11-12 10:21:17 Mathematical logic Quantification Logic Semantics Peano axioms Symbol Constructible universe Universal quantification Interpretation Uniform boundedness principle Witness Combinatory logic
5	Herbrand’s theorem and extractive proof theory U. Kohlenbach Department of Mathematics Technische Universit¨at Darmstadt Schlossgartenstrasse 7, 64289 Darmstadt, Germany September 1, 2008 Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2008-09-01 05:59:33 Mathematics Mathematical analysis Mathematical logic Functions and mappings Computability theory Primitive recursive function Recursion Theory of computation First-order logic Limit of a function Peano axioms Spectral theory of ordinary differential equations
6	FOUNDATIONAL AND MATHEMATICAL USES OF HIGHER TYPES ULRICH KOHLENBACH† DEDICATED TO SOLOMON FEFERMAN FOR HIS 70TH BIRTHDAY §1. Introduction. A central theme of proof theory is expressed by the following question: Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2012-11-12 10:34:29 Computability theory Proof theory Mathematical logic Metalogic Reverse mathematics Primitive recursive functional Second-order arithmetic Peano axioms Primitive recursive function Primitive recursive arithmetic Model theory Symbol
7	On uniform weak K¨onig’s lemma Ulrich Kohlenbach BRICS∗ Department of Computer Science University of Aarhus Ny Munkegade Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2012-11-16 09:11:16 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
8	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
9	École Doctorale de l’École polytechnique I NRIA THÈSE DE DOCTORAT Présentée par Add to Reading List Source URL: cedeela.fr Language: English - Date: 2015-10-28 05:35:30 Mathematical logic Mathematics Logic Boolean algebra First-order logic Propositional calculus FO Quantifier Boolean satisfiability problem True quantified Boolean formula Model theory Peano axioms
10	Notre Dame Journal of Formal Logic Volume 50, Number 1, 2009 Factorization of the Shoenfield-like Bounded Functional Interpretation Jaime Gaspar Add to Reading List Source URL: jg.sdf.org Language: English - Date: 2016-05-02 10:01:00 Mathematics Mathematical logic Logic Logic in computer science Constructible universe Peano axioms Factorization Algebraic logic Dialectica interpretation Combinatory logic