# Minimal lambda-theories by ultraproducts

@inproceedings{Bucciarelli2012MinimalLB, title={Minimal lambda-theories by ultraproducts}, author={Antonio Bucciarelli and Alberto Carraro and Antonino Salibra}, booktitle={Workshop on Logical and Semantic Frameworks with Applications}, year={2012} }

A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lb or the least sensible lambda-theory H (generated by equating all the unsolvable terms). A related question is whether, given a class of lambda models, there is a minimal lambda-theory represented by it. In this paper, we give a general tool to answer positively to this question and we apply it to a wide class of webbed models…

## 3 Citations

### A graph-easy class of mute lambda-terms

- MathematicsICTCS
- 2014

An infinite set S of mute terms is defined, and it is shown that it is graph-easy: for any closed term t of the lambda calculus there exists a graph model equating all the terms of S to t.

### Algebraic structures for the lambda calculus and the propositional logic

- Mathematics
- 2016

Part I Among the unsolvable terms of the lambda calculus, the mute ones are those having the highest degree of undefinedness. For each natural number n ≥ 1, we introduce two infinite and recursive…

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