Skip to content

The Proof Theory Blog

PA ⊢ ∀x ∃y A(x,y) ⇒ ∃t . T ⊢ ∀x A(x,t(x))

Menu
  • Home
  • About
  • Contribute
  • Resources
Menu

Sam Sanders

The Biggest Five of Reverse Mathematics

Posted on January 12, 2023January 12, 2023 by Sam Sanders

TL;DR: Dag Normann and I have obtained LOTS of equivalences between the second-order Big Five of Reverse Mathematics and third-order theorems from mainstream analysis about (possibly) discontinuous functions, working in Kohlenbach’s higher-order Reverse Mathematics. We also show that slight generalisations or variations of the aforementioned third-order theorems fall FAR outside of the Big Five. Our…

Read more

The computational content of Nonstandard Analysis

Posted on July 1, 2020July 1, 2020 by Sam Sanders

We discuss the computational content of Nonstandard Analysis based on recent proof-theoretic developments.

Read more

Lifting proofs: from Specker sequences to nets

Posted on May 30, 2020June 1, 2020 by Sam Sanders

This post provides an answer to the question: Can we somehow ‘lift’ proofs in a restricted language to interesting proofs in a richer language?

Read more

Of representations of mathematics

Posted on May 24, 2020June 1, 2020 by Sam Sanders

Studying mathematics via logic implies one needs to choose a suitable logical language and represent part of mathematics therein. This post deals with the question whether such representations remain true to the original, or somehow distort it. I show that even the well-known representation of continuous functions leads to significant distortion.

Read more

Meta

  • Register
  • Log in
  • Entries RSS
  • Privacy Policy

Search

© 2023 The Proof Theory Blog | Powered by Minimalist Blog WordPress Theme
The Proof Theory Blog uses cookies, but you can opt-out if you wish. For further information see our privacy policy. Cookie settingsAccept
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these cookies, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may have an effect on your browsing experience.
Necessary
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
Non-necessary
Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.
SAVE & ACCEPT