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A CO-ANALYTIC COHEN-INDESTRUCTIBLE MAXIMAL COFINITARY GROUP
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- Journal:
- The Journal of Symbolic Logic / Volume 82 / Issue 2 / June 2017
- Published online by Cambridge University Press:
- 19 June 2017, pp. 629-647
- Print publication:
- June 2017
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- Article
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Assuming that every set is constructible, we find a
${\text{\Pi }}_1^1 $ maximal cofinitary group of permutations of 
$\mathbb{N}$ which is indestructible by Cohen forcing. Thus we show that the existence of such groups is consistent with arbitrarily large continuum. Our method also gives a new proof, inspired by the forcing method, of Kastermans’ result that there exists a 
${\text{\Pi }}_1^1 $ maximal cofinitary group in L.
A co-analytic maximal set of orthogonal measures
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- Journal:
- The Journal of Symbolic Logic / Volume 75 / Issue 4 / December 2010
- Published online by Cambridge University Press:
- 12 March 2014, pp. 1403-1414
- Print publication:
- December 2010
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- Article
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We prove that if V = L then there is a
maximal orthogonal (i.e., mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.
maximal orthogonal (i.e., mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.