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NONMEASURABLE SETS AND UNIONS WITH RESPECT TO TREE IDEALS
Published online by Cambridge University Press: 19 June 2020
Abstract
In this paper, we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals
$s_0$
,
$m_0$
,
$l_0$
,
$cl_0$
,
$h_0,$
and
$ch_0$
. We show that there exists a subset of the Baire space
$\omega ^\omega ,$
which is s-, l-, and m-nonmeasurable that forms a dominating m.e.d. family. We investigate a notion of
${\mathbb {T}}$
-Bernstein sets—sets which intersect but do not contain any body of any tree from a given family of trees
${\mathbb {T}}$
. We also obtain a result on
${\mathcal {I}}$
-Luzin sets, namely, we prove that if
${\mathfrak {c}}$
is a regular cardinal, then the algebraic sum (considered on the real line
${\mathbb {R}}$
) of a generalized Luzin set and a generalized Sierpiński set belongs to
$s_0, m_0$
,
$l_0,$
and
$cl_0$
.
Keywords
- Type
- Articles
- Information
- Copyright
- © The Association for Symbolic Logic 2020
References
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