Ábrázolható

Ábrázolható is a Hungarian term that translates to "representable" or "depictable" in English, often used in the context of mathematical logic and set theory. The concept originates from the work of Hungarian mathematician Alfréd Rényi and is closely related to the idea of cardinality and the representability of sets within a given mathematical framework.

In set theory, a set is considered ábrázolható if it can be represented or mapped onto another set in a way that preserves certain structural properties. This notion is particularly relevant in discussions about the cardinality of infinite sets and the limitations of classical set theory, such as those posed by the continuum hypothesis. The term reflects the idea that some infinite sets may not be "depictable" or constructible within standard axiomatic systems, such as Zermelo-Fraenkel (ZF) set theory with the axiom of choice (ZFC).

The concept of ábrázolható is also tied to the study of constructible universes, introduced by Paul Cohen and Kurt Gödel. In this context, a set is ábrázolható if it belongs to the constructible hierarchy (denoted as L), meaning it can be built step-by-step using the axioms of ZF. Sets not in L are considered "non-constructible" or "unrepresentable" within this framework. This distinction is crucial in understanding the independence results of the continuum hypothesis and other major problems in set theory.

The term has been used in philosophical discussions about the nature of mathematical existence and the boundaries of formal systems. It highlights the tension between what can be explicitly constructed or represented within a given theory and what might exist beyond its reach. While ábrázolható is primarily a technical term in advanced mathematics, its implications touch on broader questions about the limits of mathematical knowledge and representation.