https://github.com/andrejbauer/notes-on-realizability

Lecture notes on realizability
https://github.com/andrejbauer/notes-on-realizability

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Lecture notes on realizability

• Host: GitHub
• URL: https://github.com/andrejbauer/notes-on-realizability
• Owner: andrejbauer
• Created: 2022-03-04T08:51:35.000Z (over 2 years ago)
• Default Branch: master
• Last Pushed: 2024-04-03T16:28:41.000Z (8 months ago)
• Last Synced: 2024-04-03T17:50:21.851Z (8 months ago)
• Language: TeX
• Size: 13.2 MB
• Stars: 63
• Watchers: 5
• Forks: 4
• Open Issues: 2
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  • Readme: README.md

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README

        
# Notes on realizability

This repository contains a draft of notes on realizability theory in the [`notes`](./notes) folder. You may download a [**recent PDF version of the notes**](http://www.andrej.com/zapiski/MGS-2022/notes-on-realizability.pdf).

The folder [`reading`](./reading) contains classic historical papers and other useful publications about realizability.

# Midlands graduate school 2022

The notes are the main reading material for the [Midlands Graduate School 2022](https://www.cs.nott.ac.uk/~psznk/events/mgs22.html) lecture series on realizability.

## Lecture 1: Models of computation

**Time:** Sunday, April 10, 2022, 14:00–15:00

**Contents:**

* some models of computation

* partial combinatory algebras

* assemblies

**Reading material:** The chapter “Models of computation” from the [notes](http://www.andrej.com/zapiski/MGS-2022/notes-on-realizability.pdf).

**Exercises:** (Monday, April 11, 2022, 10:30–11:25)

Consult “Lecture 1” of the [exercise sheet](http://www.andrej.com/zapiski/MGS-2022/mgs-exercises.pdf).

## Lecture 2: Realizability categories

**Time:** Monday, April 11, 2022, 14:00–15:00

**Contents:**

* modest assemblies

* equivalent formulations

* examples of assemblies

* the categorical structure of assemblies

**Reading material:** The chapter “Realiability categories” from the [notes](http://www.andrej.com/zapiski/MGS-2022/notes-on-realizability.pdf).

**Exercises:** (Tuesday, April 12, 2022, 10:30–11:25)

Consult “Lecture 2” of the [exercise sheet](http://www.andrej.com/zapiski/MGS-2022/mgs-exercises.pdf).

## Lecture 3: Realizability and type theory

**Time:** Tuesday, April 12, 2022, 14:00–15:00

**Contents:**

* families of assemblies

* products and sums of assemblies

* propositions as assemblies

* the identity type

* universes of assemblies

**Reading material:** The chapter “Realiability and type theory” from the [notes](http://www.andrej.com/zapiski/MGS-2022/notes-on-realizability.pdf). Disclaimer: this chapter is not complete yet.

**Exercises:** (Wednesday, April 13, 2022, 10:30–11:25)

Consult “Lecture 3” of the [exercise sheet](http://www.andrej.com/zapiski/MGS-2022/mgs-exercises.pdf).

## Lecture 4: The internal language at work

**Time:** Wednesday, April 13, 2022, 14:00–15:00

**Contents:**

* realizability logic

* the axiom of choice

* countable objects

* Church's thesis

* continuity principles

**Reading material:** The chapter “The internal language at work” from the [notes](http://www.andrej.com/zapiski/MGS-2022/notes-on-realizability.pdf). Disclaimer: this chapter is not written yet, but at least lecture notes will be published before the lecture.

**Exercises:** (Wednesday, April 13, 2022, 17:00–17:55)

Consult “Lecture 4” of the [exercise sheet](http://www.andrej.com/zapiski/MGS-2022/mgs-exercises.pdf).