“…This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). …”
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“…While NEP holds almost universally for natural intuitionistic set theories, the general existence property (EP), i.e. the property of a theory that for every existential theorem, a provably definable witness can be found, is known to fail for some prominent intuitionistic set theories such as Intuitionistic Zermelo–Fraenkel set theory (IZF) and constructive Zermelo–Fraenkel set theory (CZF). …”
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“…Summarizing, the Elementary Process Theory is a scheme of seven well-formed closed expressions, written in the mathematical language of set matrix theory – a generalization of Zermelo-Fraenkel set theory. In the physical world, these seven expressions can be interpreted as elementary principles governing the universe at supersmall scale. …”
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“…This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. …”
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“…Cohen’s first model is a model of Zermelo–Fraenkel set theory in which there is a Dedekind-finite set of real numbers, and it is perhaps the most famous model where the Axiom of Choice fails. …”
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