Herman Ruge Jervell

• Jervell, Herman Ruge (2015). Climbing Mount ε0, In  Gentzen's Centenary.  Springer Publishing Company.  ISBN 978-3-319-10102-6.  Part III.  s 301 - 315 Show summary

  Gentzen showed in his Habilitation that transfinite induction up to any ordinal <ε 0 is provable in first order arithmetic—and made a constructive justification of how to reach any ordinal <ε 0 . In his analysis Gentzen used ordinals in Cantor normal form. We shall look at ordinals as given by finite trees and then see how the climbing up to ε 0 can be justified there with methods from first order arithmetic, and methods to use where we climb above it.

• Jervell, Herman Ruge (2009). Kantiansk anskuelse og høyere aritmetikk, I: Anita Leirfall & Thor Sandmel (red.),  Enhet i mangfold. Festskrift i anledning Johan Arnt Myrstads 60-årsdag.  Unipub forlag.  ISBN 9788230311790.  artikkel.  s 201 - 218
• Jervell, Herman Ruge (2006). Constructing ordinals, In Gerhard Heinzmann & Giuseppina Ronzitti (ed.),  Constructivism: Mathematics, Logic, Philosophy and Linguistics.  Éditions KIMÉ.  ISBN 2-84174-399-3.  Kapittel.  s 5 - 20
• Jervell, Herman Ruge (2005). Finite trees as ordinals, In S.Barry Cooper; Benedikt Löwe & Leen Torenvliet (ed.),  New Computational Paradigms First Conference on Computability in Europe, CiE 2005.  Springer.  ISBN 3-540-26179-6.  Kapittel.  s 211 - 220
• Jervell, Herman Ruge (2005). Finite trees as ordinals. Lecture Notes in Computer Science (LNCS).  ISSN 0302-9743.  3526
• Jervell, Herman Ruge (2003). Appendix: Section 20.3 From a logical point of view, In Bernt Petter Stigum (ed.),  Econometrics and the Philosophy of Economics. Theory-Data Confrontations in Economics.  Princeton University Press.  ISBN 0-691-11300-9.  s 520 - 524
• Jervell, Herman Ruge (1999). Om det uendelige. Pascal som matematiker, logiker og fysiker, I: Hans Kolstad & Arild Waaler (red.),  Endelighet og evighet. 15 essays om Blaise Pascal.  Aschehoug & Co.  ISBN 82-03-18050-7. Show summary

  Blaise Pascal som matematiker, logiker og fysiker.

• Jervell, Herman Ruge (1996). From the axiom of choice to choice sequences. Nordic Journal of Philosophical Logic.  ISSN 0806-6205.  1(1), s 95- 98 Show summary

  A note describing how discussions about the axiom of choice in 1905 led to the development of choice sequences around 1910

• Jervell, Herman Ruge (1996). Thoralf Skolem: Pioneer of computational Logic. Nordic Journal of Philosophical Logic.  ISSN 0806-6205.  1(2), s 107- 117 Show summary

  Survey of Thoralf Skolems scientific works

• Jervell, Herman Ruge & Olsen, Kai A. (1985). Icons in man-machine communications. Behaviour and Information Technology.  ISSN 0144-929X.  4(3), s 249- 254 . doi: 10.1080/01449298508901805 Show summary

  In signs one sees an advantage for discovery that is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then, indeed, the labour of thought is wonderfully diminished Leibniz Icons are today used in many programming systems—to simplify man-machine communication. Does this represent something new and important or is it just a sales argument similar, for example, to the ‘removal’ of formulas in Cobol, by replacing the mathematical symbols by English words? In order to answer this question we will examine the use of icons in man-machine interfaces, comparing this usage with the q ualities of icons. In doing this we will rely on the fundamental work on signs of Charles Sanders Peirce (1839–1914) about the turn of the century (Hartshorne and Weiss 1965).

• Jervell, Herman Ruge & Olsen, Kai A. (1984). Computer and society. Computers & society.  ISSN 0095-2737.  13(4), s 17- 21 . doi: 10.1145/379518.379523

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• Jervell, Herman Ruge (2013). Modal logic. Logos Verlag Berlin.  ISBN 978-3-8325-3302-1.  103 s.
• Jervell, Herman Ruge (2013). Proof Theory. Logos Verlag Berlin.  ISBN 978-3-8325-3303-8.  129 s.
• Jervell, Herman Ruge (2012). Logic and computations. Logos Verlag Berlin.  ISBN 978-3-8325-3090-7.  130 s.
• Jervell, Herman Ruge (2004). Formal logic. A guided tour. Unipub forlag.  ISBN 82-7477-188-5.  194 s.
• Jervell, Herman Ruge (2002). Modal logikk. Unipub forlag.  ISBN 82-7477-094-3.  145 s. Show summary

  Videregående lærebok i modal logikk.

• Jervell, Herman Ruge (2001). Logikk og beregnbarhet. Unipub forlag.  ISBN 82-7477-072-2.  169 s. Show summary

  Lærebok i logikk og beregnbarhet - beregnet for begynnerstudenter ved universitet eller høyskoler

• Jervell, Herman Ruge & Olsen, Kai A. (1982). Hva datamaskiner ikke kan. Universitetsforlaget.  ISBN 8200071405.  182 s.

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• Jervell, Herman Ruge (2002). Hilbert, Borel og kampen om utvalgsaksiomet. Show summary

  For omtrent hundre år siden var det store kamper i matematikk om matematikkens grunnlag. Vi får ofte høre at det var paradoksene fra mengdelære som ble diskutert. Vi skal se at diskusjonene var mye nærmere knyttet til matematisk praksis - spesielt en diskusjon om hvilke funksjoner som var ordentlige og kunne brukes i matematikk. To av de frenmste i denne diskusjonen var Borel og Hilbert - og vi skal se at en god del interessant matematikk kom ut av dette.

• Jervell, Herman Ruge (2002). Review: Alasdair Urquhart: The complexity of linear logic with weakening. Bulletin of Symbolic Logic.  ISSN 1079-8986.  8, s 100- 101 Show summary

  Review of Alasdair Urquhart: The complexity of linear logic with weakening.

• Jervell, Herman Ruge (2002). The importance of indirect arguments. Show summary

  A direct argument is an argument where the intermediate steps are contained within the premisses or the conclusion. This has been explained by the notion of normal derivation or by cut-free derivation. An indirect argument is an argument which is not necessarily direct. We discuss cases where the tension between direct and indirect arguments have been important : Archimedes sandreckoner - or how to count the sandgrains in the universe, distinction between analysis and synthesis, consistency of formal systems.

• Jervell, Herman Ruge (2001). Abstractions and Metaphors on the Internet. Show summary

  Abstractions and metaphors seem necessary for human and software agents to operate on the Internet. We hear about (virtual) desktops, classrooms, universities, sales rooms, shopping baskets, etc. We investigate this from a logical point of view emphasizing the syntax/semantics distinction and the use of abstractions to handle logical and computational complexity.

• Jervell, Herman Ruge (2001). How to wellorder finite trees. Show summary

  We describe ordinal notations in the tradition of Ackermann - Schütte - Takeuti.

• Jervell, Herman Ruge & Zhang, Wenhui (2001). Cut formulas for Kalmar elementary functions. Show summary

  We show that for every Kalmar elementary function we can find appropriate cut-formulas and using them we find proofs of length linear in the arguments of the function in predicate logic of the well definedness of the function. The usual proof of cut elimination shows the converse. This gives a new characterization of the Kalmar elementary functions as the functions which we can feasibly prove to be well defined in predicate logic using cut.

• Jervell, Herman Ruge (2000). Review "Helmut Schwichtenberg: Finite notations for infinite terms.". Bulletin of Symbolic Logic.  ISSN 1079-8986.  6(4), s 477- 477 Show summary

  Review of paper

• Jervell, Herman Ruge (1999). On the limitations of logic programming. Show summary

  This is joint work with Wenhui Zhang. We prove that to every Kalmar elementary function there are cut formulas giving a proof of length linear in the arguments proving that the function is well defined. The converse follows by well known arguments. This gives both a neww characterization of the Kalmar elementary functions and a limitation of what can be feasibly proved in logic programming - even using interactive proofs.

• Jervell, Herman Ruge (1995). Dynamic Datastructures. Show summary

  We give the connection between Solomon Fefermans replete, relative categorical ordinal notations and Jean-Yves Girards dilators.

• Jervell, Herman Ruge (1995). Informatikk som fag. Vitenskapsteoretisk belyst. Show summary

  Grunnlagsmessige probleme i informatikk.

• Jervell, Herman Ruge & Olsen, Kai A. (1980). Hva datamaskiner ikke kan. Dagbladet.  ISSN 0805-3766.

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