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A universal continuum of weight |
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| Authors: | Alan Dow Klaas Pieter Hart |
| Affiliation: | Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3 ; Faculty of Technical Mathematics and Informatics, TU Delft, Postbus 5031, 2600 GA Delft, The Netherlands |
| Abstract: | We prove that every continuum of weight We complement this result by showing that 1) under We also show that a universal continuum can be gotten from a |
| Keywords: | Paroviv{c}enko's theorem universal continuum remainder of $[0 infty)$ $aleph_1$-saturated model elementary equivalence Continuum Hypothesis Cohen reals long segment Martin's Axiom Proper Forcing Axiom saturated ultrafilter |
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is a continuous image of the Cech-Stone-remainder 
of the real line. It follows that under 
the remainder of the half line 
is universal among the continua of weight 
-- universal in the `mapping onto' sense. 
every continuum of weight less than 
is a continuous image of 
, 2) in the Cohen model the long segment of length 
is not a continuous image of 
, and 3) 
implies that 
is not a continuous image of 
, whenever 
is a 
-saturated ultrafilter. 
-saturated ultrafilter on 
, and that it is consistent that there is no universal continuum of weight 
.