Constructibility

Part of the book series: Universitext ((UTX))

Abstract

We introduce Gödel’s constructible universe L and the class HOD and prove key results about these models.

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1.
Recall from p. 12 that \(\mathsf{ZFC}^-\) is ZFC without the power set axiom.
2.
I.e., \(\chi _R({\varvec{x})}=1\) iff \(R({\varvec{x})}\) and \(=0\) otherwise.
3.
Here, \(\mathrm{Lim}\) denotes the class of all limit ordinals.
4.
Here, \(x\) is not assumed to be transitive.
5.
\(a \cap b= a {\setminus } (a {\setminus } b)\).
6.
We assume w.l.o.g. that every \(g_i\), \(1\le i \le \ell \), is \(k\)-ary.
7.
The reason why the functions \(F_9\) through \(F_{15}\) were added to the above list is in fact to guarantee that if \(U\) is transitive, then \(\mathbf{S}^E(U)\) is transitive as well.
8.
we pretend that all \(F_i\), \(i<17\), are binary.

Institut für Mathematische Logik und Gru, Universität Münster, Münster, Germany
Ralf Schindler

Authors

Ralf Schindler
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Correspondence to Ralf Schindler .

Schindler, R. (2014). Constructibility. In: Set Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-06725-4_5