## Set-Theoretical and Other Elementary Models of the lambda-calculus (1993)

Venue: | Theoretical Computer Science |

Citations: | 40 - 0 self |

### BibTeX

@ARTICLE{Plotkin93set-theoreticaland,

author = {Gordon Plotkin},

title = {Set-Theoretical and Other Elementary Models of the lambda-calculus},

journal = {Theoretical Computer Science},

year = {1993},

volume = {121},

pages = {351--409}

}

### Years of Citing Articles

### OpenURL

### Abstract

Part 1 of this paper is the previously unpublished 1972 memorandum [43], with editorial changes and some minor corrections. Part 2 presents what happened next, together with some further development of the material. The first part begins with an elementary set-theoretical model of the fi-calculus. Functions are modeled in a similar way to that normally employed in set theory, by their graphs; difficulties are caused in this enterprise by the axiom of foundation. Next, based on that model, a model of the fij-calculus is constructed by means of a natural deduction method. Finally, a theorem is proved giving some general properties of those non-trivial models of the fij-calculus which are continuous complete lattices. The second part begins with a brief discussion of models of the -calculus in set theories with anti-foundation axioms. Next the model of the fi- calculus of Part 1 and also the closely related---but different!---models of Scott [53, 54] and of Engeler [21, 22] are reviewed....