Skip to content

The Proof Theory Blog

Γ, A ⊢ B ⇒ Γ ⊢ A → B

Menu
  • Home
  • About
  • Contribute
  • Resources
Menu

Category: Uncategorized

Syntactic Proofs of the Analytic Cut Property

Posted on September 5, 2023September 6, 2023 by Timo Lang

An instance of the cut rule is called analytic if the cut formula already appears as a subformula of the lower sequent. For example, the cut is analytic because the cut formula is contained in . Analytic cut can be seen as a deep inference rule. In classical and modal logic it corresponds to a…

Read more

Second-order-ish mathematics I

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

The English language uses the modifier “-ish” for “sort of”. A “sort of yellow” object is called “yellow-ish”. This post describes a class of third-order objects that are “sort of second-order”, i.e. second-order-ish. First of all, fix a function on the reals that is continuous everywhere and a real . A moment of thought reveals…

Read more

Countable sets in the wild

Posted on May 8, 2023May 9, 2023 by Sam Sanders

TL;DR: there are various definitions of the notion ‘countable set of reals’ and only one seems to lead to nice equivalences in Reverse Mathematics. In particular, injections and bijections to the naturals à la Cantor are not very suitable. A slightly more general notion leads to many equivalences involving regulated and bounded variation functions, as…

Read more

On representations and their brute-forced connections.

Posted on March 13, 2023March 14, 2023 by Sam Sanders

TL;DR: classical Reverse Mathematics makes heavy use of so-called codes or representations. We observe a major problem with this coding practise, namely the connection between open sets and continuous functions, which is ‘brute-forced’ by the coding of these objects. The long version: Reverse Mathematics needs no introduction on this blog and neither does , the…

Read more
  • 1
  • 2
  • 3
  • 4
  • …
  • 7
  • Next

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