While it is known that any $c$-spanner is also both a weak $C_1$-spanner and a $C_2$-power spanner (for appropriate $C_1,C_2$ depending only on $c$ but not on the graph under consideration), we show that the converse fails: There exists a family of $c_1$-power spanners that are no weak $C$-spanners and also a family of weak $c_2$-spanners that are no $C$-spanners for any fixed $C$ (and thus no uniform spanners, either). However the deepest result of the present work reveals that, surprisingly, any weak spanner is also a uniform power spanner. We further generalize the latter notion by considering $(c,delta)$-power spanners where the sum of the $delta$-th powers of the lengths has to be bounded; so $(cdot,2)$-power spanners coincide with the usual power spanners and $(cdot,1)$-power spanners are classical spanners. Interestingly, these $(cdot,delta)$-power spanners form a strict hierarchy where the above results still hold for any $deltageq2$; some even hold for $delta>1$ while counterexamples reveal others to fail for $delta<2$. In fact we show that in general every self-similar curve of fractal dimension $d>delta$ is no $(C,delta)$-power spanner for any fixed $C$. AU - Schindelhauer, Christian AU - Volbert, Klaus AU - Ziegler, Martin ID - 18279 SN - 0302-9743 T2 - Proc. of 15th Annual International Symposium on Algorithms and Computation (ISAAC'04) TI - Spanners, Weak Spanners, and Power Spanners for Wireless Networks VL - 3341 ER - TY - JOUR AU - Tophinke, Doris ID - 18281 JF - Infodienst. Kulturpädagogische Nachrichten TI - Quatschwörterverse und Satzklötze. Sprachförderung im Kindergarten VL - 71 ER - TY - GEN AU - Peckhaus, Volker ID - 18495 T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1033.03002] TI - Newen, Albert/Nortmann, Ulrich/Stuhlmann-Laeisz, Rainer (Hgg.), Building on Frege. New Essays on Sense, Content, and Concept, CSLI Publications: Standford, CA 2001 ER - TY - GEN AU - Peckhaus, Volker ID - 18488 T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1030.01030] TI - Takeuti, Gaisi, Memoirs of a Proof Theorist. Gödel and other Logicians, ed. Mariko Yasugi/Nicholas Passell, World Scientific: New Jersey u.a. 2003 ER - TY - GEN AU - Peckhaus, Volker ID - 18483 T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1026.03006] TI - Tomassi, Paul, “Logic after Wittgenstein,” Nordic Journal of Philosophical Logic 6 (2001), 43–70 ER - TY - GEN AU - Peckhaus, Volker ID - 18490 T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1030.03005] TI - Baker, G.P./P.M.S. Hacker, “Functions in Begriffsschrift”, Synthese 135 (2003), 273–297 ER - TY - GEN AU - Peckhaus, Volker ID - 18503 T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1048.00002] TI - Dörfler, Willi, „Über die Fiktionalität mathematischer Objekte“, Mathematische Semesterberichte 48 (2002), 123–138 ER -