Abstract
The basics of descriptive set theory get developed.
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Notes
- 1.
Here, \(n^\frown t{^{\prime }}\) is that sequence which starts with \(n\), followed by \(t{^{\prime }}(0), \ldots , t{^{\prime }}(\mathrm{lh}(t{^{\prime }})-1)\). This notation as well as self-explaining variants thereof will frequently be used in what follows.
- 2.
We here write \(s \bot t\) iff \(s\) and \(t\) are incomparable, i.e., \(s \upharpoonright (\mathrm{lh}(s) \cap \mathrm{lh}(t)) \not = t \upharpoonright (\mathrm{lh}(s) \cap \mathrm{lh}(t))\). Also, \(<_\mathrm{lex}\) is the lexicographic ordering.
- 3.
In what follows, \(Q\) is \(\exists \) or \(\forall \) depending on whether \(n\) is odd or even.
- 4.
By identifying \(n<\omega \) with the constant function \(c_n :\omega \rightarrow \omega \) with value \(n\), we may construe \(({}^{\omega }\omega )^k\times \omega \) as a subset of \(({}^{\omega }\omega )^{k+1}\).
- 5.
Here, \((x)_0\) and \((x)_1\) are defined to be the unique reals such that \((x)_0 \oplus (x)_1 = x\).
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© 2014 Springer International Publishing Switzerland
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Schindler, R. (2014). Descriptive Set Theory. In: Set Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-06725-4_7
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DOI: https://doi.org/10.1007/978-3-319-06725-4_7
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