There are many ways to construct denotational models of PCF.
The original model presented by Scott and Plotkin used domain-theoretic techniques to interpret recursion. The construction predates both of them, and is essentially due to Platek.
However, there are many models of PCF with a non-domain-theoretic flavour. However, because of the presence of recursion, such models invariably contain of some kind of domain-theoretic structure somewhere - even if that only consists of least upper bound of rational chains.
The following styles of model have been used:
The most general description of a model of PCF can be found by straightforwardly translating the typing rules to category theory
In short, it consists of a cartesian closed category that supports a bunch of constants of the appropriate type, satisfying the equational theory that is induced by the operational semantics.
An explicit description of that may be found in [Hyland and Ong 2000].
Please expand.
Hyland, J.M.E., and C.-H.L. Ong. 2000. “On Full Abstraction for PCF: I, II, and III.” Information and Computation 163 (2): 285–408. https://doi.org/10.1006/inco.2000.2917.
@article{Hyland2000,
author = {Hyland, J.M.E. and Ong, C.-H.L.},
doi = {10.1006/inco.2000.2917},
issn = {08905401},
journal = {Information and Computation},
number = {2},
pages = {285--408},
title = {On Full Abstraction for PCF: I, II, and III},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0890540100929171},
volume = {163},
year = {2000}
}