# A family of ${2}^{{\aleph}_{1}}$ logarithmic functions of distinct growth rates

Open Mathematics (2010)

- Volume: 8, Issue: 6, page 1026-1028
- ISSN: 2391-5455

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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

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- [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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