How did Russell’s theory of types try to avoid logical paradoxes?

Bertrand Russell’s theory of types was developed to resolve logical contradictions, most notably Russell’s paradox, which arises when a system allows for the unrestricted construction of sets or predicates that refer to themselves.123

To prevent these paradoxes, Russell introduced a hierarchical structure:

• Simple Theory of Types: This approach mandates that a set or predicate of a certain logical type can only contain or apply to entities of a lower type. By prohibiting a set from being a member of itself, the system avoids the self-referential contradictions inherent in the "set of all sets that are not members of themselves".23
• Ramified Theory of Types: Russell and Alfred North Whitehead further addressed "impredicative" definitions—where an object is defined by a quantifier that includes the object itself—by applying the vicious circle principle. This principle forbids defining an object by means of a totality to which the object itself belongs, leading to a more complex, stratified hierarchy of higher-order objects.23

Because this ramified structure was restrictive, they introduced the axiom of reducibility to allow for the derivation of standard mathematics.23