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Peano axioms
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21	LOGIC AND THE METHODOLOGY OF SCIENCE PRELIMINARY EXAMINATION 1. Let L = L(F1 ) be the first-order language having exactly one unary function symbol and no constant or relation symbols. Give examples of infinite L-structu Add to Reading List Source URL: logic.berkeley.edu Language: English - Date: 2014-08-24 16:43:20 Model theory First-order logic Predicate logic Peano axioms Constructible universe Ordinal number Ω-consistent theory Surreal number Mathematical logic Logic Mathematics
22	Zenon Modulo: When Achilles Outruns the Tortoise using Deduction Modulo? David Delahaye1 , Damien Doligez2 , Frédéric Gilbert2 , Pierre Halmagrand1 , and Olivier Hermant3 1 Add to Reading List Source URL: bware.lri.fr Language: English - Date: 2014-09-27 11:16:17 Logic in computer science Unification First-order logic Combinatory logic Rewriting Model theory Axiom Mathematical proof Peano axioms Logic Mathematics Mathematical logic
23	[hal, v1] Zenon Modulo: When Achilles Outruns the Tortoise using Deduction Modulo Add to Reading List Source URL: www.cri.ensmp.fr Language: English - Date: 2014-01-28 10:05:43 Logic in computer science Unification First-order logic Combinatory logic Rewriting Model theory Axiom Mathematical proof Peano axioms Logic Mathematics Mathematical logic
24	The Peirce Translation Mart´ın Escard´o University of Birmingham, UK Paulo Oliva Queen Mary University of London, UK Add to Reading List Source URL: www.cs.bham.ac.uk Language: English - Date: 2011-06-09 07:02:59 Logic in computer science Proof theory Adjoint functors Gödel–Gentzen negative translation Monad Intuitionistic logic Quantification Peano axioms Witness Logic Mathematical logic Mathematics
25	System T and the Product of Selection Functions Martín Escardó1 , Paulo Oliva2 , and Thomas Powell2 1 University of Birmingham Department of Computer Science Add to Reading List Source URL: www.cs.bham.ac.uk Language: English - Date: 2011-06-20 06:36:33 Proof theory Computability theory Functions and mappings Theory of computation Dialectica interpretation Function Primitive recursive function Peano axioms Well-founded relation Mathematics Mathematical logic Logic
26	Do the Integers Exist? The Unknowability of Arithmetic Consistency JACK T. SCHWARTZ Courant Institute It is an article of faith for most mathematicians that Peano’s axioms for arithmetic are consistent, perhaps becaus Add to Reading List Source URL: www.multimedialibrary.com Language: English - Date: 2005-12-01 07:11:01 Axiom Mathematical proof Foundations of mathematics Peano axioms Kurt Gödel Contradiction Zermelo–Fraenkel set theory Theorem Gottlob Frege Logic Mathematics Mathematical logic
27	I. Intro II. Avoiding Counting Assignments III. Avoiding Alignment Add to Reading List Source URL: www.pfeifer-research.de Language: English - Date: 2013-09-18 05:16:04 Philosophy of mathematics Logicism Axiom Peano axioms Probability Mathematical proof Mathematics Mathematical logic Logic
28	Empiricism, Probability, and Knowledge of Arithmetic Sean Walsh, Department of Logic and Philosophy of Science, University of California, Irvine The topic of this paper is the tenability of a certain type of empiricism a Add to Reading List Source URL: www.pfeifer-research.de Language: English - Date: 2013-05-16 13:22:33 Proof theory Logic in computer science Computability theory Effective descriptive set theory Peano axioms Logicism Second-order arithmetic Philosophy of mathematics Axiom Mathematics Mathematical logic Logic
29	Open-endedness, schemas and ontological commitment∗ Nikolaj Jang Pedersen and Marcus Rossberg December 10, 2008 Abstract Second-order axiomatizations of certain important mathematical theories – such as arithmetic an Add to Reading List Source URL: www.nikolajpedersen.com Language: English - Date: 2010-02-17 05:11:03 Predicate logic Model theory Quantification Analytic philosophers First-order logic George Boolos Second-order arithmetic Peano axioms Second-order logic Logic Mathematical logic Mathematics
30	COMPUTER SCIENCE TRIPOS Part IA – 2014 – Paper 2 9 Discrete Mathematics (AMP) (a) The subset S of N = {0, 1, 2, . . .} is inductively defined by the following axiom and rules, where n ranges over N: Add to Reading List Source URL: www.cl.cam.ac.uk Language: English - Date: 2014-06-09 10:18:43 Mathematical proofs Inductive reasoning Mathematical induction Proof theory Constructible universe Universal quantification String Surreal number Peano axioms Mathematics Mathematical logic Logic