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Questions tagged [consistency-strength]

Use this tag when discussing the relative logical strength of axiom sets or foundations of theorem provers

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An unexpectedly hard question about type equality (of sigma types)

Suppose you have A: Type and P Q: A -> Prop such that {x : A | P x} = {x : A | Q x}. Can ...
15 votes
3 answers

What is known about the consistency of proof assistant metatheories?

I realised I don't know the status of consistency of theorem provers' metatheories - what is currently known? For example, as far as I know Lean's type theory is equiconsistent to ZFC+countably many ...
13 votes
1 answer

Attempts to accommodate theories of different consistency strength in single assistant

TL;DR: How / where to formalize results concerning the logical strength of systems? Are proof assistants having a weak base theory but also enough infrastructure to make it feasible? I'll start by ...
20 votes
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Can we automatically get around set-theoretic difficulties?

One of the main technical annoyances of working with (large) categories is the variety of set-theoretic difficulties that come about with it: if we use ZFC as background logic, then those large ...