A family of $$ 2^{\aleph _1 } $$ logarithmic functions of distinct growth rates

• Autorzy: Salma Kuhlmann
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Germs of real valued functions; Growth rate; Asymptotic scale; Lexicographic order; Automorphims of ordered sets

Kategorie tematyczne

• 03C60: Model-theoretic algebra
• 06A05: Total order

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 6
• Strony: 1026-1028

Daty

wydano

2010-12-01

online

2010-10-30

Twórcy

autor

Salma Kuhlmann

• Universität Konstanz

Bibliografia

• [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
• [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
• [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
• [6] Steprāns J., History of the continuum in the 20th century, Handb. Hist. Log., 6 (in press)

Identyfikatory

DOI

10.2478/s11533-010-0070-z