Finite type structures within combinatory algebras (Q1182485)

Inside a combinatory algebra (ca), the author defines certain intensional and extensional type structures over \(\omega\). (Note: in the definition of \(ET_{n+1}\) a subscript 0 is missing from =.) If these classes coincide the algebra is called ft-extensional. Criteria for ft- extensionality are given and some well known ca's including \(D_ A,\;P_ \omega,\;T^ \omega,\;H_ \omega\) and certain \(D_ \infty\)-models are shown to be ft-extensional. Examples of ca's without this property are given. Finally ft-extensionality is compared to and shown to be independent of extensionality and weak extensionality.