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Peano axioms
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31	Emperors, dragons, and other mathematicalia Wolfgang Schwarz 02 February 2005 Abstract. One of the most intriguing applications of possibilia is the reduction of mathematical truths. I argue that this is no Add to Reading List Source URL: www.umsu.de Language: English Elementary mathematics Z notation Model theory Formal systems Peano axioms Axiom Philosophy of mathematics Gottlob Frege Logicism Mathematics Mathematical logic Logic
32	This sentence does not contain the symbol X Samuel A. Alexander∗ Department of Mathematics, the Ohio State University To appear in The Reasoner. In order to formalize the Liar’s Paradox, one approach is as follows. W Add to Reading List Source URL: www.semitrivial.com Language: English - Date: 2013-06-28 11:56:13 Diagonal lemma Peano axioms Function Well-formed formula Symbol Constructible universe Non-standard model of arithmetic Interpretation Mathematics Logic Mathematical logic
33	Commentary/Rips et al.: From numerical concepts to concepts of number arithmetical skills. However, they neglect the neo-Fregean alternative axiomatization of arithmetic, based on Hume’s principle. Frege arithmetic is Add to Reading List Source URL: users.ox.ac.uk Language: English - Date: 2013-10-08 12:52:07 Numbers Mathematical logic Elementary arithmetic Philosophy of mathematics Peano axioms Gottlob Frege Numeracy Negative number Natural number Mathematics Elementary mathematics Integers
34	Lecture 1: Induction and the Natural numbers Math 1a is a somewhat unusual course. It is a proof-based treatment of Calculus, for all of you who have already demonstrated a strong grounding in Calculus at the high school Add to Reading List Source URL: math.caltech.edu Language: English - Date: 2013-06-28 11:42:54 Inductive reasoning Mathematical induction Proof theory Series Well-order Number Peano axioms Summation Ordinal number Mathematics Mathematical logic Mathematical proofs
35	Reverse Mathematics Benedict Eastaugh December 13, 2011 In ordinary mathematical practice, mathematicians prove theorems, reasoning from a fixed1 set of axioms to a logically derivable conclusion. The axioms in play are Add to Reading List Source URL: extralogical.net Language: English - Date: 2014-05-22 10:36:49 Proof theory Model theory Z notation Formal systems Reverse mathematics Second-order arithmetic Peano axioms Zermelo–Fraenkel set theory Ordinal analysis Logic Mathematical logic Mathematics
36	Models for Substructural Arithmetics Greg Restall School of Philosophy The University of Melbourne1 [removed] http://consequently.org/writing/mfsa Add to Reading List Source URL: www.consequently.org Language: English - Date: 2007-06-26 05:31:00 Model theory Non-classical logic Algebraic structures Equivalence relation Philosophical logic Congruence relation Peano axioms First-order logic Relevance logic Logic Mathematical logic Mathematics
37	For Oystein Linnebo, ed., special number of Synthese on Bad Company FOCUS RESTORED Comment on John MacFarlane’s “Double Vision: Two Questions about the Neo-Fregean Programme” Bob Hale and Crispin Wright Add to Reading List Source URL: as.nyu.edu Language: English - Date: 2011-02-17 15:42:39 Analytic philosophers Philosophers of mathematics Philosophy of mathematics Elementary mathematics Crispin Wright Logicism Gottlob Frege Function Peano axioms Mathematics Logic Mathematical logic
38	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
39	Models for Substructural Arithmetics Greg Restall School of Philosophy The University of Melbourne1 [removed] http://consequently.org/writing/mfsa Add to Reading List Source URL: consequently.org Language: English - Date: 2007-06-26 05:31:00 Model theory Non-classical logic Algebraic structures Equivalence relation Philosophical logic Congruence relation Peano axioms First-order logic Relevance logic Logic Mathematical logic Mathematics
40	Etica & Politica / Ethics & Politics, 2003, 1 Add to Reading List Source URL: www2.units.it Language: English - Date: 2004-01-28 05:21:56 Proof theory Model theory Logic in computer science Metalogic Peano axioms Soundness Axiom Function Consistency Logic Mathematics Mathematical logic