@article {IOPORT.04016892,
    author       = {Weitkamp, Galen},
    title        = {On the existence and recursion theoretic properties of $\Sigma \sp 1\sb n$-generic sets of reals.},
    year         = {1985},
    journal      = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik},
    volume       = {31},
    issn         = {0044-3050},
    pages        = {97-108},
    publisher    = {VEB Deutscher Verlag der Wissenschaften, Berlin},
    doi          = {10.1002/malq.19850310702},
    abstract     = {For $\Phi$ being any subset of the power set of the Baire space $\sp{\omega}\omega$, the author defines the notion of $\Phi$-generic set of reals and investigates its recursion-theoretic properties. Main results of the paper concern the case $\Phi =\Sigma\sp 1\sb 1$, the class of all analytic subsets of $\sp{\omega}\omega$. Some of the most interesting results are: A $\Sigma\sp 1\sb 1$-generic set neither contains nor is disjoint from a perfect set. $\Sigma$ ${}\sp 1\sb 1$-generic sets are nonmeasurable. If the Continuum Hypothesis is assumed, then $\Sigma\sp 1\sb 1$-generic sets exist. The validity of the converse to the last statement is an open problem, but there are some results of similar character proven in the last section of the paper, e.g.: The existence of a $\Sigma\sp 0\sb 1$-generic set is consistent with $ZFC+2\sp{\aleph\sb 0}=\aleph\sb 2$.},
    reviewer     = {A.Wojciechowska},
    identifier   = {04016892},
}