DeepAI AI Chat
Log In Sign Up

Should Type Theory replace Set Theory as the Foundation of Mathematics

11/11/2021
by   Thorsten Altenkirch, et al.
0

We discuss why Type Theory is preferable as foundation of Mathematics compared to set theory.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/09/2023

Pure Data Foundation of Mathematics and Computing

We propose an axiomatic foundation of mathematics based on the finite se...
05/12/2020

MathZero, The Classification Problem, and Set-Theoretic Type Theory

AlphaZero learns to play go, chess and shogi at a superhuman level throu...
04/20/2018

Formalising Mathematics In Simple Type Theory

Despite the considerable interest in new dependent type theories, simple...
05/28/2020

Adding an Abstraction Barrier to ZF Set Theory

Much mathematical writing exists that is, explicitly or implicitly, base...
09/14/2022

LibertyMFD: A Lexicon to Assess the Moral Foundation of Liberty

Quantifying the moral narratives expressed in the user-generated text, n...
06/24/2022

Ranks, copulas, and permutons

We review a recent development at the interface between discrete mathema...
05/03/2019

Game Semantics of Martin-Löf Type Theory

We present game semantics of Martin-Löf type theory (MLTT), which solves...