Although this book deals with basic set theory (in general, it stops short of areas where
model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. …

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands
of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there …

1. Introduction, and statement of the results. One of the most remarkable features of the
axiom of choice of ZF is that it is equivalent to many different statements taken from various …

Let ZFM be the set theory ZF together with an axiom which asserts the existence of a measurable
cardinal. It is shown that if ZFM is consistent then ZFM is consistent with every sentence …

§ 7. Undecidable sentences 30 § 8. The syntactical hierarchy theorems 36 $9. Reflection
phenomena 48 $10. The lower levels of the hierarchy 51 Appendix A. The dependence of the …

AZRIEL LEVY l Introduction. There are, in general, two main approaches to the introduction
of strong infinity assertions to the Zermelo-Fraenkel set theory. The arithmetical approach …

This paper analyses the relationship between the efficient sets of investment portfolios and
the investment holding period. Investors are allowed to hold risky assets as well as the …

It was shown in [4] that the Zermelo-Fraenkel set theory may be obtained by adjoining to the
Zermelo theory Z an axiom schema called the principle of complete reflection.(This schema, …

Publisher Summary This chapter discusses the definability in axiomatic set theory. If Zermelo-Fraenkel
(ZF) set theory is consistent, so is ZF with the axiom of choice added (ZFC) + …

The aim of the present paper is to provide some additional information on the size of the
indescribable cardinals of Hanf and Scott [1]. The major tool which we shall use will be the …