Dag Normann

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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
Other affiliations Department for Informatics

Current Project

I am currently working on an informal joint project with Sam Sanders, where we analyse theorems and constructions in classical mathematics from the viewpoints of Kohlenbach's higher order reverse mathematics and higher order computability theory.

Tags: Mathematics, Logic

Publications

  • Normann, Dag & Sanders, Sam (2022). On the uncountability of R. Journal of Symbolic Logic (JSL). ISSN 0022-4812. p. 1–45. doi: 10.1017/jsl.2022.27.
  • Normann, Dag & Sanders, Sam (2021). Betwixt Turing and Kleene. Lecture Notes in Computer Science (LNCS). ISSN 0302-9743. 13137, p. 236–252. doi: 10.1007/978-3-030-93100-1_15. Full text in Research Archive
  • 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. 31(1), p. 297–325. doi: 10.1093/logcom/exaa080.
  • 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 (2020). Measure-theoretic Uniformity and the Suslin Functional. Computability - The Journal of the Assosiation. ISSN 2211-3568. 10(2), p. 91–105. doi: 10.3233/COM-190248. Full text in Research Archive
  • 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 & 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 (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 & 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 (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 (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 (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). 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 (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 (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 (2006). Computing with functionals - Computability theory or computer science? Bulletin of Symbolic Logic. ISSN 1079-8986. 12(1), p. 43–59.
  • Normann, Dag (2006). On sequential functionals of type 3. Mathematical Structures in Computer Science. ISSN 0960-1295. 16, p. 279–289.
  • 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). Exact real number computations relative to hereditarily total functionals. Theoretical Computer Science. ISSN 0304-3975. 284, p. 437–453.
  • Normann, Dag & Geir, Waagbø (2002). Limit spaces and transfinite types. Archive for Mathematical Logic. ISSN 0933-5846. 41, p. 525–539.
  • 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 (2002). Representation theorems for transfinite computability and definability. Archive for Mathematical Logic. ISSN 0933-5846. 41, p. 721–741.
  • Normann, Dag (2002). Continuity, proof systems and the theory of transfinite computations. Archive for Mathematical Logic. ISSN 0933-5846. 41, p. 765–788.

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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 (2022). A recent development in the computability theory for functionals of type 3.
  • Normann, Dag (2022). Typed lambda calculus and operators of mainstream mathematics.
  • Normann, Dag (2022). The complexity of operators constructed in mainstream mathematics.
  • Normann, Dag & Sanders, Sam (2022). Betwixed Turing and Kleene.
  • Normann, Dag (2021). An alternative perspective on Reverse Mathematics.
  • Normann, Dag (2019). The Computational Complexity of the Heine Borel Theorem.
  • Normann, Dag (2018). Functionals of Type 3 as Realisers of Classical Theorems in Analysis.
  • 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). 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). Alan Turing - mer enn en kodebryter.
  • Normann, Dag (2015). Var Turing oppfinneren av datamaskinen?
  • Normann, Dag (2015). Abels tårn. [Radio]. NRK.
  • 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). Sequential versus Continuous Models of Finite Types.
  • Normann, Dag (2011). Fixed point computability of total functionals.
  • Normann, Dag (2011). Banach spaces as data types.
  • Normann, Dag (2011). Om Urysohns universelle metriske rom - og litt om Urysohn selv.
  • Normann, Dag (2009). The sequential functionals are far from being algebraic domains.
  • Normann, Dag (2009). Sequential Functionals at Type level 2.
  • Normann, Dag (2009). Finite Sequential Procedures with Observational Ordering.
  • Normann, Dag (2009). Functionals of finite types - bridging logic and computer science.
  • Normann, Dag (2009). Continuous vs. Sequential Functionals - Harmony or Disharmony?
  • Normann, Dag (2009). Computations and functionals of finite types.
  • 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). External and internal density theorems for limspace-interpretations of some types.
  • Normann, Dag (2007). Hvor vanskelig kan det være? Om bondesjakk og det å finne maksimumspunktet til en kontinuerlig funksjon.
  • 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). Domain theory based hierarchies of total functionals.
  • Normann, Dag (2006). The coincidense problem and its topological counterpart.
  • Normann, Dag (2006). On sequential functionals of type 3.
  • Normann, Dag (2006). The Continuous Functionals and Aspects of Computability.
  • Normann, Dag (2005). Regning ved hjelp av tallerkenstabler - en innfallsvinkel til programmeringsteori.
  • Normann, Dag (2005). Minesveiper - hva har det med matematikk å gjøre.
  • 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 (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). Regning ved hjelp av tallerkenstabler - en innfallsvinkel til programmeringsteori.
  • Normann, Dag (2004). Minesveiper -hva har det med matematikk å gjøre.
  • Normann, Dag (2004). Er du en kløpper i Minesveiper og kan bevise det, kan du bli en million dollar rikere.
  • Normann, Dag (2004). Minesveiper er NP-komplett.
  • 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). Sammenhengen mellom klassiske paradokser og datamaskiners lunefullhet.
  • Normann, Dag (2001). Definability of total objects in PCF and related calculi.
  • Normann, Dag (2001). Definability and totality in typed lambda-calculi.
  • 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). Platonske legemer.

View all works in Cristin

Published Nov. 30, 2010 11:20 PM - Last modified Jan. 25, 2022 1:39 PM