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Primitive recursive arithmetic
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1	REMARKS ON FINITISM W. W. TAIT† The background of these remarks is that in 1967, in ‘’Constructive reasoning” [27], I sketched an argument that ﬁnitist arithmetic coincides with primitive recursive arithmetic, Add to Reading List Source URL: home.uchicago.edu Language: English - Date: 2001-09-04 16:12:18
2	Primitive Recursive Arithmetic and its Role in the Foundations of Arithmetic: Historical and Philosophical Reflections In Honor of Per Martin-L¨ of on the Occasion of His Retirement Add to Reading List Source URL: home.uchicago.edu Language: English - Date: 2014-10-08 11:39:14
3	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
4	A note on the Π02–induction rule∗ Ulrich Kohlenbach Fachbereich Mathematik, J.W.Goethe-Universit¨at, Robert-Mayer-Strasse 6–10, D–60054 Frankfurt, Germany Abstract It is well–known (due to C. Parsons) that th Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2012-11-16 10:10:40 Predicate logic Computability theory Recursion Logic Theory of computation Primitive recursive arithmetic Primitive recursive function Quantifier First-order logic Free variables and bound variables Herbrandization
5	Real Growth in Standard Parts of Analysis∗ Ulrich Kohlenbach Fachbereich Mathematik J.W. Goethe Universit¨at Robert-Mayer-StrFrankfurt am Main, Germany Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2014-04-08 12:00:27 Computability theory Functions and mappings Recursion Theory of computation Proof theory Primitive recursive function Continuous function Elementary function arithmetic Arithmetic function
6	G¨odel functional interpretation and weak compactness Ulrich Kohlenbach1 Department of Mathematics Technische Universit¨at Darmstadt Schlossgartenstraße 7, 64289 Darmstadt, Germany -darmstadt.d Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2011-08-31 12:29:01 Mathematics Mathematical analysis Operator theory Computability theory Arithmetic function Primitive recursive function Ergodic theory Hilbert space Theoretical physics Spectral theory of ordinary differential equations Differential forms on a Riemann surface
7	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
8	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
9	Things that can and things that can’t be done in PRA Ulrich Kohlenbach BRICS∗ Department of Computer Science University of Aarhus Ny Munkegade, Bldg. 540 Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2012-11-16 09:11:59 Computability theory Mathematical logic Mathematics Theoretical computer science Primitive recursive function Primitive recursive arithmetic ELEMENTARY Reverse mathematics Pairing function Ackermann function Sequence Recursion
10	BRICS Basic Research in Computer Science BRICS RSU. Kohlenbach: On the No-Counterexample Interpretation On the No-Counterexample Interpretation Add to Reading List Source URL: www.mathematik.tu-darmstadt.de Language: English - Date: 2012-11-16 09:12:20 Mathematical logic Logic Proof theory Computability theory Mathematics Constructivism Primitive recursive functional First-order logic Symbol Primitive recursive function Primitive recursive arithmetic Realizability

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