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A very slow growing hierarchy for

from RESEARCH ARTICLES

Published online by Cambridge University Press:  30 March 2017

Jan Van Eijck
Affiliation:
Centre for Mathematics and Computer Science, Amsterdam
Vincent Van Oostrom
Affiliation:
Universiteit Utrecht, The Netherlands
Albert Visser
Affiliation:
Universiteit Utrecht, The Netherlands
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Logic Colloquium '99 , pp. 182 - 199
Publisher: Cambridge University Press
Print publication year: 2004

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References

[1] A., Beckmann, S., Buss, and C., Pollett, Ordinal notations and well-orderings in bounded arithmetic, Annals of Pure and Applied Logic, vol. 120, no. 1-3.
[2] Benjamin, Blankertz and Andreas, Weiermann, How to characterize provably total functions by the Buchholz operator method, Gödel ‘96 (Brno. 1996) (PetrHájek, editor), Lecture Notes in Logic, vol. 6, Springer, Berlin, 1996, pp. 205-213.
[3] Wilfried, Buchholz, E., Adam Cichon, and Andreas, Weiermann, A uniform approach to fundamental sequences and hierarchies,Mathematical Logic Quarterly, vol. 40 (1994), pp. 273- 286.Google Scholar
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[8] Helmut, Vogel, Ausgezeichnete Folgen für prädikative Ordinalzahlen und prädikativrekursive Funktionen, Zeitschrift fürMathematische Logik undGrundlagen derMathematik, vol. 23 (1977), no. 5, pp. 435-438.Google Scholar
[9] Stanley, ScottWainer, Slow growing versus fast growing, The Journal of Symbolic Logic, vol. 54 (1989), no. 2, pp. 608-614.Google Scholar
[10] Stanley, ScottWainer, Accessible segments of the fast growing hierarchy, Logic colloquium ‘95 (Haifa), Springer, Berlin, 1998, pp. 339-348.
[11] Andreas, Weiermann, How to characterize provably total functions by local predicativity, The Journal of Symbolic Logic, vol. 61 (1996), no. 1, pp. 52-69.Google Scholar
[12] Andreas, Weiermann, Sometimes slow growing is fast growing, Annals of Pure and Applied Logic, vol. 90 (1997), no. 1-3, pp. 91-99.Google Scholar
[13] Andreas, Weiermann, How is it that infinitary methods can be applied to finitary mathematics? Goedel's T: A case study, The Journal of Symbolic Logic, vol. 63 (1998), no. 4, pp. 1348-1370.Google Scholar
[14] Andreas, Weiermann, What makes a (pointwise) subrecursive hierarchy slow growing?, Sets and proofs (Cambridge) (S., Barry Cooper et al., editors), London Mathematical Society Lecture Notes, vol. 258, Cambridge University Press, 1999, pp. 403-423.
[15] Andreas, Weiermann, A very slow growing hierarchy for the Howard Bachmann ordinal, preprint, Münster, 2000.
[16] Andreas, Weiermann, Γ0 may be subrecursively inaccessible, Mathematical Logic Quarterly, vol. 47 (2001), pp. 397-408.Google Scholar
[17] Andreas, Weiermann, Some interesting connections between the slow growing hierarchy and the Ackermann function, The Journal of Symbolic Logic, vol. 66 (2001), pp. 609-628.Google Scholar
[18] Andreas, Weiermann, Slow versus fast growing, Synthese, vol. 133 (2002), pp. 13-19.Google Scholar

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