A family of logarithmic functions of distinct growth rates
Open Mathematics (2010)
- Volume: 8, Issue: 6, page 1026-1028
- ISSN: 2391-5455
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Abstract
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topSalma Kuhlmann. "A family of \[ 2^{\aleph _1 } \] logarithmic functions of distinct growth rates." Open Mathematics 8.6 (2010): 1026-1028. <http://eudml.org/doc/269601>.
@article{SalmaKuhlmann2010,
abstract = {We construct a totally ordered set Γ of positive infinite germs (i.e. germs of positive real-valued functions that tend to +∞), with order type being the lexicographic product ℵ1 × ℤ2. We show that Γ admits \[ 2^\{\aleph \_1 \} \]
order preserving automorphisms of pairwise distinct growth rates.},
author = {Salma Kuhlmann},
journal = {Open Mathematics},
keywords = {Germs of real valued functions; Growth rate; Asymptotic scale; Lexicographic order; Automorphims of ordered sets; germs of real-valued functions; growth rate; asymptotic scale; lexicographic order; automorphims of ordered sets},
language = {eng},
number = {6},
pages = {1026-1028},
title = {A family of \[ 2^\{\aleph \_1 \} \] logarithmic functions of distinct growth rates},
url = {http://eudml.org/doc/269601},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Salma Kuhlmann
TI - A family of \[ 2^{\aleph _1 } \] logarithmic functions of distinct growth rates
JO - Open Mathematics
PY - 2010
VL - 8
IS - 6
SP - 1026
EP - 1028
AB - We construct a totally ordered set Γ of positive infinite germs (i.e. germs of positive real-valued functions that tend to +∞), with order type being the lexicographic product ℵ1 × ℤ2. We show that Γ admits \[ 2^{\aleph _1 } \]
order preserving automorphisms of pairwise distinct growth rates.
LA - eng
KW - Germs of real valued functions; Growth rate; Asymptotic scale; Lexicographic order; Automorphims of ordered sets; germs of real-valued functions; growth rate; asymptotic scale; lexicographic order; automorphims of ordered sets
UR - http://eudml.org/doc/269601
ER -
References
top- [1] Hardy G.H., Orders of Infinity; The ‘Infinitärcalcül’ of Paul Du Bois-Reymond, Cambridge Tracts in Math. and Math. Physics, 12, Cambridge University Press, Cambridge, 1954
- [2] Hausdorff F., Die Graduierung nach dem Endverlauf, Abhandlungen der Königl. Sächs. Ges. der Wiss. zu Leipzig. Math.-Phys. Klasse, 1909, 31, 295–334 Zbl40.0446.02
- [3] Kojman M., History of singular cardinals in the 20th century: from Hausdorff’s gap to Shelah’s PCF theory, Handb. Hist. Log., 6 (in press)
- [4] Kuhlmann S., Ordered Exponential Fields, Fields Inst. Monogr., 12, American Mathematical Society, Providence, 2000 Zbl0989.12003
- [5] Kuhlmann S., Shelah S., κ-bounded exponential-logarithmic power series fields, Ann. Pure Appl. Logic, 2005, 136(3), 284–296 http://dx.doi.org/10.1016/j.apal.2005.04.001 Zbl1079.03024
- [6] Steprāns J., History of the continuum in the 20th century, Handb. Hist. Log., 6 (in press)
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