Dag Normann

Image of Dag Normann
Norwegian version of this page
Phone +47 22855953
Mobile phone +47 41 25 02 05
Username
Visiting address Moltke Moes vei 35 Niels Henrik Abels hus 0851 OSLO
Other affiliations Department of Mathematics

Current Project

Countably based functionals as realisers for classical theorems in analysis.

Tags: Mathematics, Logic

Publications

  • Normann, Dag & Sanders, Sam (2020). Pincherle's theorem in reverse mathematics and computability theory. Annals of Pure and Applied Logic.  ISSN 0168-0072. . doi: https://doi.org/10.1016/j.apal.2020.102788
  • Normann, Dag & Sanders, Sam (2019). Computability Theory, Nonstandard Analysis, and Their Connections. Journal of Symbolic Logic (JSL).  ISSN 0022-4812.  84(4), s 1422- 1465 . doi: 10.1017/jsl.2019.69
  • 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), s 1- 42 . doi: 10.1016/j.apal.2019.05.007
  • Normann, Dag (2018). Functionals of Type 3 as Realisers of Classical Theorems in Analysis, In Florin Manea; Russel G. Miller & Dirk Nowotka (ed.),  Sailing Routes in the World of Computation.  Springer Nature.  ISBN 978-3-319-94417-3.  kapittel.  s 318 - 327
  • 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(1:23)2018 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 & Tait, William (2017). On the Computability of the Fan Functional, In Gerhard Jäger & Wilfried Sieg (ed.),  Feferman on Foundations Logic, Mathematics, Philosophy.  Springer Nature.  ISBN 978-3-319-63332-9.  del 1 - kapittel 3.  s 57 - 70
  • 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), s 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(1:8)2015
  • Normann, Dag (2014). Higher Generalizations of the Turing Model, In Rod Downey (ed.),  Turing's Legacy: Developments from Turing's Ideas in Logic.  Cambridge University Press.  ISBN 978-1-107-04348-0.  kapittel 11.  s 397 - 433
  • Normann, Dag (2012). The Continuous Functionals as Limit Spaces, In Ulrich Berger; Hannes Diener; Peter Schuster & Monika Seisenberger (ed.),  Logic, Construction, Computation.  Ontos Verlag.  ISBN 978-3-86838-158-0.  kapittel 17.  s 353 - 379
  • Normann, Dag & Sazonov, Vladimir Yu. (2012). The extensional ordering of the sequential functionals. Annals of Pure and Applied Logic.  ISSN 0168-0072.  163(5), s 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(2:11)2011
  • Normann, Dag (2011). Experiments on an Internal Approach to Typed Algorithms in Analysis, In Barry Cooper & Andrea Sorbi (ed.),  Computability in Context. Computation and Logic in the Real World.  Imperial College Press.  ISBN 978-1-84816-245-7.  Kapittel 9.  s 297 - 327
  • 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(3:11)2009
  • Normann, Dag (2008). Applications of the Kleene-Kreisel Density Theorem to Theoretical Computer Science, In S. Barry Cooper; Benedikt Løwe & Andrea Sorbi (ed.),  New Computational Paradigms; Changing Conceptions of What is Computable.  Springer Publishing Company.  ISBN 978-0-387-36033-1.  Kapittel.  s 119 - 138
  • Normann, Dag (2008). Internal Density Theorems for Hierarchies of Continuous Functionals, In Arnold* Beckmann; Costas Dimitracopoulos & Benedikt Löwe (ed.),  Logic and Theory of Algorithms.  Springer.  ISBN 978-3-540-69405-2.  kapittel.  s 467 - 475
  • Normann, Dag (2006). Definability and Reducibility in Higher Types over the Reals, In Viggo Stoltenberg-Hansen & Jouko Väänänen (ed.),  LOGIC COLLOQUIUM´03.  Association for Symbolic Logic.  ISBN 1-56881-293-0.  Artikkel.  s 200 - 220
  • Normann, Dag (2006). Computing with functionals - Computability theory or computer science?. Bulletin of Symbolic Logic.  ISSN 1079-8986.  12(1), s 43- 59
  • Normann, Dag (2006). On sequential functionals of type 3. Mathematical Structures in Computer Science.  ISSN 0960-1295.  16, s 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(2)2005 Show summary
  • 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, s 141- 147 Show summary
  • Normann, Dag (2004). Hierarchies of total functionals over the reals. Theoretical Computer Science.  ISSN 0304-3975.  316, s 137- 151
  • Normann, Dag (2002). Continuity, proof systems and the theory of transfinite computations. Archive for Mathematical Logic.  ISSN 0933-5846.  41, s 765- 788 Show summary
  • Normann, Dag (2002). Exact real number computations relative to hereditarily total functionals. Theoretical Computer Science.  ISSN 0304-3975.  284, s 437- 453 Show summary
  • Normann, Dag (2002). Om å velge den rette modell for beregnbarhet over de reelle tallene. Normat.  ISSN 0801-3500.  49(3), s 97- 104 Show summary
  • Normann, Dag (2002). Representation theorems for transfinite computability and definability. Archive for Mathematical Logic.  ISSN 0933-5846.  41, s 721- 741 Show summary
  • Normann, Dag & Geir, Waagbø (2002). Limit spaces and transfinite types. Archive for Mathematical Logic.  ISSN 0933-5846.  41, s 525- 539 Show summary
  • Normann, Dag & Rørdam, Christian (2002). The Computational Power of M^omega. Mathematical logic quarterly.  ISSN 0942-5616.  48(1), s 117- 124 Show summary
  • Normann, Dag (2000). Computability over the partial continuous functionals. Journal of Symbolic Logic (JSL).  ISSN 0022-4812.  65(3), s 1133- 1142 Show summary
  • Normann, Dag (2000). The Cook-Berger Problem. A Guide to the solution. Electronical Notes in Theoretical Computer Science.  ISSN 1571-0661.  35 Show summary
  • Normann, Dag (2000). The continuous functionals of finite types over the reals. Electronical Notes in Theoretical Computer Science.  ISSN 1571-0661. Show summary

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

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  • Normann, Dag (2019). The Computational Complexity of the Heine Borel Theorem.
  • 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 (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 (2016). Revisiting Transfinite Types.
  • Normann, Dag (2015, 02. januar). Abels tårn. [Radio].  NRK. Show summary
  • Normann, Dag (2015). Alan Turing - mer enn en kodebryter. Show summary
  • 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), s 509- 510 . doi: 10.1016/j.apal.2013.02.001
  • Normann, Dag (2012). Internal or external, abstract or concrete? What does this mean for computing in a Banach space?.
  • Normann, Dag (2012). Sequential vs. Continuous Functionals of Finite types.
  • Normann, Dag (2011). Banach spaces as data types.
  • Normann, Dag (2011). Fixed point computability of total functionals.
  • Normann, Dag (2011). Om Urysohns universelle metriske rom - og litt om Urysohn selv.
  • Normann, Dag (2011). Sequential versus Continuous Models of Finite Types.
  • Normann, Dag (2009). Computations and functionals of finite types.
  • Normann, Dag (2009). Continuous vs. Sequential Functionals - Harmony or Disharmony?.
  • Normann, Dag (2009). Finite Sequential Procedures with Observational Ordering.
  • Normann, Dag (2009). Functionals of finite types - bridging logic and computer science.
  • Normann, Dag (2009). Sequential Functionals at Type level 2.
  • Normann, Dag (2009). The sequential functionals are far from being algebraic domains. Show summary
  • 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.
  • Normann, Dag (2006). Domain theory based hierarchies of total functionals.
  • Normann, Dag (2006). On sequential functionals of type 3.
  • Normann, Dag (2006). The Continuous Functionals and Aspects of Computability.
  • Normann, Dag (2006). The coincidense problem and its topological counterpart.
  • Cooper, Barry; Löwe, Benedikt & Normann, Dag (2006). Mathematics of computing at CiE 2005. Mathematical Structures in Computer Science.  ISSN 0960-1295.  16(5), s 735- 736
  • 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), s 21- 27
  • Normann, Dag (2005). Regning ved hjelp av tallerkenstabler - en innfallsvinkel til programmeringsteori.
  • Normann, Dag (2005). Sequential functionals of type 3.
  • Normann, Dag (2004). Er du en kløpper i Minesveiper og kan bevise det, kan du bli en million dollar rikere.
  • Normann, Dag (2004). Er du en kløpper i Minesveiper og kan bevise det, kan du bli en million dollar rikere. Show summary
  • Normann, Dag (2004). Minesveiper - hva har det med matematikk å gjøre?. Show summary
  • Normann, Dag (2004). Minesveiper er NP-komplett. Show summary
  • Normann, Dag (2004). Minesveiper -hva har det med matematikk å gjøre.
  • Normann, Dag (2004). Regning ved hjelp av tallerkenstabler - en innfallsvinkel til programmeringsteori. Show summary
  • Normann, Dag (2004). Turings verden - lag dine egne datamaskiner. Show summary
  • Normann, Dag (2004). Typed Computability over discrete and continuous base types.
  • Normann, Dag (2003). Computability in higher type functionals: History, challenges and results,. Show summary
  • Normann, Dag (2003). Er du en kløpper i minesveiper, og kan bevise det, kan du bli en million dollar rikere. Show summary
  • Normann, Dag (2003). The continuous functionals in the perspective of domain theory. Show summary
  • Normann, Dag (2002). Hierarchies of total functionals over the reals. Show summary
  • Normann, Dag (2002). Om deterministiske og ikke-deterministiske beregninger. Show summary
  • Normann, Dag (2001). Definability and totality in typed lambda-calculi. Show summary
  • Normann, Dag (2001). Definability of total objects in PCF and related calculi. Show summary
  • Normann, Dag (2001). Sammenhengen mellom klassiske paradokser og datamaskiners lunefullhet. Show summary
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Platonske legemer.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (2000). Spillteori.
  • Normann, Dag (1999). Computability over the partial continuous functionals. Show summary
  • Normann, Dag (1999). Computable objects in typed structures. Show summary
  • Normann, Dag (1999). Computing the Computable Functionals. Show summary

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Published Nov. 30, 2010 11:20 PM - Last modified Nov. 20, 2018 11:51 AM