# On Choice Rules in Dependent Type Theory

@inproceedings{Maietti2017OnCR, title={On Choice Rules in Dependent Type Theory}, author={Maria Emilia Maietti}, booktitle={TAMC}, year={2017} }

In a dependent type theory satisfying the propositions as types correspondence together with the proofs-as-programs paradigm, the validity of the unique choice rule or even more of the choice rule says that the extraction of a computable witness from an existential statement under hypothesis can be performed within the same theory.

## 6 Citations

Quantifier completions, choice principles and applications.

- Philosophy
- 2020

We give an expositional account of the quantifier completions by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and…

Elementary quotient completions : a brief

- Philosophy
- 2019

Hyland’s effective topos offers an important realizability model for constructive mathematics in the form of a category whose internal logic validates Church’s Thesis. It also contains a boolean full…

Choice principles via the existential completion

- Mathematics
- 2020

It is well know that choice principles, such as Zermelo’s axiom of choice, are not generally valid in constructive foundations for mathematics which include quotient sets. Also Hilbert’s epsilon…

The G\"odel Fibration

- Philosophy
- 2021

We introduce the notion of a Gödel fibration, which is a fibration categorically embodying both the logical principle of traditional Skolemization (we can exchange the order of quantifiers paying the…

The Compatibility of the Minimalist Foundation with Homotopy Type Theory

- Mathematics
- 2022

The Minimalist Foundation, for short MF , is a two-level foundation for constructive mathematics ideated by Maietti and Sambin in 2005 and then fully formalized by Maietti in 2009. MF serves as a…

Elementary Quotient Completions, Church's Thesis, and Partioned Assemblies

- PhilosophyLog. Methods Comput. Sci.
- 2019

The effective topos and the quasitopos of assemblies as elementary quotient completions of Lawvere doctrines based on partitioned assemblies are compared to explain why the two forms of (CT) each one satisfies differ as inherited from specific properties of the doctrine which determines each Elementary quotient completion.

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One could also mention the field of Model Theory, where new axioms of Set Theory may play an important role in the development of algebra.