Dag Normann

Image of Dag Normann
Norwegian version of this page
Mobile phone +47 41 25 02 05
Username
Visiting address Gaustadalléen 23B Ole-Johan Dahls hus 0373 Oslo
Postal address Postboks 1080 Blindern 0316 Oslo

Current Project

Countably based functionals as realisers for classical theorems in analysis.

Tags: Mathematics, Logic

Publications

  • Normann, Dag & Sanders, Sam (2021). The Axiom of Choice in computability theory and Reverse Mathematics with a cameo for the Continuum Hypothesis. Journal of Logic and Computation. ISSN 0955-792X. doi: 10.1093/logcom/exaa080.
  • Normann, Dag & Sanders, Sam (2020). Pincherle's theorem in reverse mathematics and computability theory. Annals of Pure and Applied Logic. ISSN 0168-0072. 171(5). doi: 10.1016/j.apal.2020.102788. Full text in Research Archive
  • Normann, Dag (2020). Measure-theoretic Uniformity and the Suslin Functional. Computability - The Journal of the Assosiation. ISSN 2211-3568. doi: 10.3233/COM-190248. Full text in Research Archive
  • Normann, Dag & Sanders, Sam (2020). Open sets in computability theory and reverse mathematics. Journal of Logic and Computation. ISSN 0955-792X. 30(8), p. 1639–1679. doi: 10.1093/logcom/exaa049.
  • Normann, Dag & Sanders, Sam (2019). Computability Theory, Nonstandard Analysis, and Their Connections. Journal of Symbolic Logic (JSL). ISSN 0022-4812. 84(4), p. 1422–1465. doi: 10.1017/jsl.2019.69. Full text in Research Archive
  • Normann, Dag & Sanders, Sam (2019). The strength of compactness in Computability Theory and Nonstandard Analysis. Annals of Pure and Applied Logic. ISSN 0168-0072. 170(11), p. 1–42. doi: 10.1016/j.apal.2019.05.007. Full text in Research Archive
  • Normann, Dag & Sanders, Sam (2018). On the mathematical and foundational significance of the uncountable. Journal of Mathematical Logic. ISSN 0219-0613. 18(2). doi: 10.1142/S0219061319500016. Full text in Research Archive
  • Normann, Dag (2018). Functionals of Type 3 as Realisers of Classical Theorems in Analysis. In Manea, Florin; Miller, Russel G. & Nowotka, Dirk (Ed.), Sailing Routes in the World of Computation. Springer Nature. ISSN 978-3-319-94417-3. p. 318–327. doi: 10.1007/978-3-319-94418-0_32. Full text in Research Archive
  • Normann, Dag (2018). The sequential functionals of type $(\iota \rightarrow \iota)^n \rightarrow \iota$ form a dcpo for all $n \in {\mathbb N}$. Logical Methods in Computer Science. ISSN 1860-5974. 14(1). doi: 10.23638/LMCS-14%281%3A23%292018. Full text in Research Archive
  • Normann, Dag & Tait, William (2017). On the Computability of the Fan Functional. In Jäger, Gerhard & Sieg, Wilfried (Ed.), Feferman on Foundations Logic, Mathematics, Philosophy. Springer Nature. ISSN 978-3-319-63332-9. p. 57–70. doi: 10.1007/978-3-319-63334-3_3.
  • Normann, Dag (2016). On the Cantor-Bendixson rank of a set that is searchable in Gödel's T. Computability - The Journal of the Assosiation. ISSN 2211-3568. 5(1), p. 61–74. doi: 10.3233/COM-150043. Full text in Research Archive
  • Normann, Dag (2015). The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems. Logical Methods in Computer Science. ISSN 1860-5974. 11(1). doi: 10.2168/LMCS-11%281%3A8%292015.
  • Normann, Dag (2014). Higher Generalizations of the Turing Model. In Downey, Rod (Eds.), Turing's Legacy: Developments from Turing's Ideas in Logic. Cambridge University Press. ISSN 978-1-107-04348-0. p. 397–433. doi: 10.1017/cbo9781107338579.012.
  • Normann, Dag & Sazonov, Vladimir Yu. (2012). The extensional ordering of the sequential functionals. Annals of Pure and Applied Logic. ISSN 0168-0072. 163(5), p. 575–603. doi: 10.1016/j.apal.2011.06.013.
  • Normann, Dag (2012). The Continuous Functionals as Limit Spaces. In Berger, Ulrich; Diener, Hannes; Schuster, Peter & Seisenberger, Monika (Ed.), Logic, Construction, Computation. Ontos Verlag. ISSN 978-3-86838-158-0. p. 353–379. doi: 10.1515/9783110324921.353.
  • Normann, Dag (2011). Experiments on an Internal Approach to Typed Algorithms in Analysis. In Cooper, Barry & Sorbi, Andrea (Ed.), Computability in Context. Computation and Logic in the Real World. Imperial College Press. ISSN 978-1-84816-245-7. p. 297–327. doi: 10.1142/9781848162778_0009.
  • Normann, Dag (2011). Banach spaces as data types. Logical Methods in Computer Science. ISSN 1860-5974. 7(2). doi: 10.2168/LMCS-7%282%3A11%292011.
  • Normann, Dag (2009). A rich hierarchy of functionals of finite types. Logical Methods in Computer Science. ISSN 1860-5974. 5(3). doi: 10.2168/LMCS-5%283%3A11%292009.
  • Normann, Dag (2008). Internal Density Theorems for Hierarchies of Continuous Functionals. In Beckmann, Arnold*; Dimitracopoulos, Costas & Löwe, Benedikt (Ed.), Logic and Theory of Algorithms. Springer. ISSN 978-3-540-69405-2. p. 467–475.
  • Normann, Dag (2008). Applications of the Kleene-Kreisel Density Theorem to Theoretical Computer Science. In Cooper, S. Barry; Løwe, Benedikt & Sorbi, Andrea (Ed.), New Computational Paradigms; Changing Conceptions of What is Computable. Springer Publishing Company. ISSN 978-0-387-36033-1. p. 119–138.
  • Normann, Dag (2006). On sequential functionals of type 3. Mathematical Structures in Computer Science. ISSN 0960-1295. 16, p. 279–289.
  • Normann, Dag (2006). Computing with functionals - Computability theory or computer science? Bulletin of Symbolic Logic. ISSN 1079-8986. 12(1), p. 43–59.
  • Normann, Dag (2006). Definability and Reducibility in Higher Types over the Reals. In Stoltenberg-Hansen, Viggo & Väänänen, Jouko (Ed.), LOGIC COLLOQUIUM´03. Association for Symbolic Logic. ISSN 1-56881-293-0. p. 200–220.
  • Normann, Dag (2005). Comparing hierarchies of total functionals. Logical Methods in Computer Science. ISSN 1860-5974. 1(2). doi: 10.2168/LMCS-1%282%292005.
  • Normann, Dag (2004). Hierarchies of total functionals over the reals. Theoretical Computer Science. ISSN 0304-3975. 316, p. 137–151.
  • Normann, Dag (2004). A Nonstandard Characterisation of the Type-structure of Continuous Functionals Over the Reals. Electronical Notes in Theoretical Computer Science. ISSN 1571-0661. 73, p. 141–147.
  • Normann, Dag & Rørdam, Christian (2002). The Computational Power of M^omega. Mathematical logic quarterly. ISSN 0942-5616. 48(1), p. 117–124.
  • Normann, Dag (2002). Om å velge den rette modell for beregnbarhet over de reelle tallene. Normat. ISSN 0801-3500. 49(3), p. 97–104.
  • Normann, Dag & Geir, Waagbø (2002). Limit spaces and transfinite types. Archive for Mathematical Logic. ISSN 0933-5846. 41, p. 525–539.
  • Normann, Dag (2002). Continuity, proof systems and the theory of transfinite computations. Archive for Mathematical Logic. ISSN 0933-5846. 41, p. 765–788.
  • Normann, Dag (2002). Representation theorems for transfinite computability and definability. Archive for Mathematical Logic. ISSN 0933-5846. 41, p. 721–741.
  • Normann, Dag (2002). Exact real number computations relative to hereditarily total functionals. Theoretical Computer Science. ISSN 0304-3975. 284, p. 437–453.
  • Normann, Dag (2000). The continuous functionals of finite types over the reals. Electronical Notes in Theoretical Computer Science. ISSN 1571-0661.
  • Normann, Dag (2000). Computability over the partial continuous functionals. Journal of Symbolic Logic (JSL). ISSN 0022-4812. 65(3), p. 1133–1142.
  • Normann, Dag (2000). The Cook-Berger Problem. A Guide to the solution. Electronical Notes in Theoretical Computer Science. ISSN 1571-0661. 35.

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  • Longley, John & Normann, Dag (2015). Higher-Order Computability. Springer. ISBN 978-3-662-47991-9. 585 p.
  • Normann, Dag; Dimitracopoulos, Costas; Newelski, Ludomir & Steel, John R. (2008). Logic Colloquium 2005. Cambridge University Press. ISBN 9780521884259. 288 p.

View all works in Cristin

  • Normann, Dag (2021). An alternative perspective on Reverse Mathematics.
  • Normann, Dag (2019). The Computational Complexity of the Heine Borel Theorem.
  • Normann, Dag (2018). David Marker, Lectures on Infinitary Model Theory. Studia Logica: An International Journal for Symbolic Logic. ISSN 0039-3215. doi: 10.1007/s11225-018-9827-3. Full text in Research Archive
  • Normann, Dag (2018). Functionals of Type 3 as Realisers of Classical Theorems in Analysis.
  • Normann, Dag (2018). A comparative study of the Heine-Borel theorem, the Lindelöf Lemma and non-monotone inductive definitions of sets of integers.
  • Normann, Dag (2016). Revisiting Transfinite Types.
  • Normann, Dag (2015). Abels tårn. [Radio]. NRK.
  • Normann, Dag (2015). Alan Turing - mer enn en kodebryter.
  • Normann, Dag (2015). Var Turing oppfinneren av datamaskinen?
  • Buss, Sam; Lowe, Benedikt; Normann, Dag & Soskov, Ivan (2013). Computability in Europe 2011 Preface. Annals of Pure and Applied Logic. ISSN 0168-0072. 164(5), p. 509–510. doi: 10.1016/j.apal.2013.02.001.
  • Normann, Dag (2012). Sequential vs. Continuous Functionals of Finite types.
  • Normann, Dag (2012). Internal or external, abstract or concrete? What does this mean for computing in a Banach space?
  • Normann, Dag (2011). Om Urysohns universelle metriske rom - og litt om Urysohn selv.
  • Normann, Dag (2011). Fixed point computability of total functionals.
  • Normann, Dag (2011). Sequential versus Continuous Models of Finite Types.
  • Normann, Dag (2011). Banach spaces as data types.
  • Normann, Dag (2009). The sequential functionals are far from being algebraic domains.
  • Normann, Dag (2009). Computations and functionals of finite types.
  • Normann, Dag (2009). Functionals of finite types - bridging logic and computer science.
  • Normann, Dag (2009). Finite Sequential Procedures with Observational Ordering.
  • Normann, Dag (2009). Continuous vs. Sequential Functionals - Harmony or Disharmony?
  • Normann, Dag (2009). Sequential Functionals at Type level 2.
  • Normann, Dag (2008). 50 years of continuous functionals.
  • Normann, Dag (2008). Om kontinuerlige operatorer på datasstrømmer og et åpent problem i topologi.
  • Normann, Dag (2008). Trenger vi uendelige mengder i diskret matematikk?
  • Normann, Dag (2007). Hvor vanskelig kan det være? Om bondesjakk og det å finne maksimumspunktet til en kontinuerlig funksjon.
  • Normann, Dag (2007). External and internal density theorems for limspace-interpretations of some types.
  • Normann, Dag (2007). Kan datamaskiner spille bondesjakk.
  • Normann, Dag (2007). Kan datamaskiner spille bondesjakk.
  • Cooper, Barry; Löwe, Benedikt & Normann, Dag (2006). Mathematics of computing at CiE 2005. Mathematical Structures in Computer Science. ISSN 0960-1295. 16(5), p. 735–736.
  • Normann, Dag (2006). On sequential functionals of type 3.
  • Normann, Dag (2006). The coincidense problem and its topological counterpart.
  • Normann, Dag (2006). The Continuous Functionals and Aspects of Computability.
  • Normann, Dag (2006). Domain theory based hierarchies of total functionals.
  • Normann, Dag (2005). Om mulige og tilsynelatende umulige programmeringsoppgaver. Normat. ISSN 0801-3500. 53(1), p. 21–27.
  • Normann, Dag (2005). Sequential functionals of type 3.
  • Normann, Dag (2005). Minesveiper - hva har det med matematikk å gjøre.
  • Normann, Dag (2005). Regning ved hjelp av tallerkenstabler - en innfallsvinkel til programmeringsteori.
  • Normann, Dag (2004). Minesveiper -hva har det med matematikk å gjøre.
  • Normann, Dag (2004). Regning ved hjelp av tallerkenstabler - en innfallsvinkel til programmeringsteori.
  • Normann, Dag (2004). Minesveiper er NP-komplett.
  • Normann, Dag (2004). Er du en kløpper i Minesveiper og kan bevise det, kan du bli en million dollar rikere.
  • Normann, Dag (2004). Minesveiper - hva har det med matematikk å gjøre?
  • Normann, Dag (2004). Turings verden - lag dine egne datamaskiner.
  • Normann, Dag (2004). Er du en kløpper i Minesveiper og kan bevise det, kan du bli en million dollar rikere.
  • Normann, Dag (2004). Typed Computability over discrete and continuous base types.
  • Normann, Dag (2003). Er du en kløpper i minesveiper, og kan bevise det, kan du bli en million dollar rikere.
  • Normann, Dag (2003). Computability in higher type functionals: History, challenges and results,
  • Normann, Dag (2003). The continuous functionals in the perspective of domain theory.
  • Normann, Dag (2002). Om deterministiske og ikke-deterministiske beregninger.
  • Normann, Dag (2002). Hierarchies of total functionals over the reals.
  • Normann, Dag (2001). Definability of total objects in PCF and related calculi.
  • Normann, Dag (2001). Sammenhengen mellom klassiske paradokser og datamaskiners lunefullhet.
  • Normann, Dag (2001). Definability and totality in typed lambda-calculi.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Platonske legemer.

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Published Nov. 30, 2010 11:20 PM - Last modified May 8, 2020 9:37 AM