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lawrencecpaulson / lawrencecpaulson.github.io

the blog "Machine Logic"
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https://lawrencecpaulson.github.io/2022/01/26/Set_theory.html #7

Open utterances-bot opened 2 years ago

utterances-bot commented 2 years ago

Machine Logic

https://lawrencecpaulson.github.io/2022/01/26/Set_theory.html

phlegmaticprogrammer commented 2 years ago

This blog provides a great source of pointers to interesting books and papers. This article for example points via one indirection to Mac Lane's "Mathematics: Form and Function", which I wasn't aware of until now!

sterraf commented 1 year ago

Concerning pieces of mathematics that require more power than Zermelo Set Theory, there is the Borel Determinacy Theorem. It belongs to Descriptive Set Theory; though "set theory" appears in the name, it can be regarded in this respect as a branch of Real Analysis.

Even before the theorem was proved, Harvey Friedman showed that it can't be done unless one assumes a substantial amount of Replacement.

lawrencecpaulson commented 1 year ago

Many thanks. This claim I can easily believe. More generally, game theory seems to require the whole of ZF. Certainly Conway's Partizan Games concept does.