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Infinite Powers and Cohen Reals
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- Journal:
- Canadian Mathematical Bulletin / Volume 61 / Issue 4 / 01 December 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 812-821
- Print publication:
- 01 December 2018
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We give a consistent example of a zero-dimensional separable metrizable space
$Z$ such that every homeomorphism of 
${{Z}^{\omega }}$ acts like a permutation of the coordinates almost everywhere. Furthermore, this permutation varies continuously. This shows that a result of Dow and Pearl is sharp, and gives some insight into an open problem of Terada. Our example $Z$ is simply the set of 
${{\omega }_{1}}$ Cohen reals, viewed as a subspace of 
${{2}^{\omega }}$.
Why Solovay real produces Cohen real
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- Journal:
- The Journal of Symbolic Logic / Volume 51 / Issue 4 / December 1986
- Published online by Cambridge University Press:
- 12 March 2014, pp. 957-968
- Print publication:
- December 1986
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