caa a22 4500 467899797 CHVBK 20180406152814.0 cr unu---uuuuu 170328e20060901xx s 000 0 eng 10.1007/s00012-006-2003-z doi (NATIONALLICENCE)springer-10.1007/s00012-006-2003-z Taylor Walter Department of Mathematics, University of Colorado, 80309-0395, Boulder, CO, USA aut Equations on real intervals [Elektronische Daten] [Walter Taylor] Abstract.: A (finite or infinite) set ∑ of equations, in operation symbols Ft (t ∈T) and variables xi, is said to be compatible with $${\user2{{\mathbb{R}}}}$$ iff there exist continuous operations FtA on $${\user2{{\mathbb{R}}}}$$ such that the algebra $${\mathbf{A}}\, = \,({\user2{{\mathbb{R}}}};\,F^{{\mathbf{A}}}_{t} )_{{t \in T}}$$ satisfies the equations ∑ (with the variables xi understood as universally quantified). It is proved that there is no algorithm to decide $${\user2{{\mathbb{R}}}}$$ -compatibility for all finite ∑. If the definition is restricted to C1 idempotent operations FtA , then there does exist an algorithm for compatibility. Birkhäuser Verlag, Basel, 2007 topological algebra nationallicence algorithm nationallicence compatibility nationallicence diophantine equation nationallicence functional equation nationallicence undecidability nationallicence differentiability nationallicence Tarski algorithm nationallicence [n]-th power variety nationallicence algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/4(2006-09-01), 409-456 0002-5240 55:4<409 2006 55 12 https://doi.org/10.1007/s00012-006-2003-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00012-006-2003-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Taylor Walter Department of Mathematics, University of Colorado, 80309-0395, Boulder, CO, USA aut NATIONALLICENCE 773 0- algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/4(2006-09-01), 409-456 0002-5240 55:4<409 2006 55 12 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer