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npx skills add https://github.com/bneb/perqed --skill forcing-set-theory-independence
Please help me install this Agent Skill. Skill: forcing_set_theory_independence Source: https://github.com/bneb/perqed/tree/main/.agents/skills/forcing_set_theory_independence Command: npx skills add https://github.com/bneb/perqed --skill forcing-set-theory-independence
This skill helps formalize and explore statements that are independent of ZFC by constructing forcing extensions and verifying which statements hold in the extended models.
Provide a minimal Lean 4 sketch showing that a statement is independent of ZFC by constructing a forcing extension.
High-intent search queries and answers about installing and using this skill.
To formalize independence proofs in set theory using Lean 4, you construct forcing extensions and verify which statements hold in the extended models, using provided templates to annotate forcing relations and generic filters against ZFC axioms.
Forcing is a technique used to construct extensions of ZFC models, allowing you to explore and verify statements that are independent of standard ZFC axioms by checking their truth in the newly forced generic models.
Yes, you can use Lean 4 to illustrate classical independence results like the Continuum Hypothesis by providing guided Lean sketches and minimal scaffolds to model the forcing notions and generic extensions.
Yes, proving ZFC independence in Lean 4 requires a forcing machinery scaffold alongside Lean 4, as these templates are necessary to properly model forcing notions and validate generic extensions.
The approach requires advanced familiarity with Lean 4 and forcing machinery, limiting its use to theoretical research and educational contexts where ZFC independence results are explicitly explored and annotated.
r-irbeGuide Lean 4 formalization with universe management and Prop/Type distinctions.
yimwooDispatch parallel subagents for 2-5 independent tasks and verify merged outputs.
my04337Plan and pre-validate Lean 4 proof strategies before theorem proving.
lightrain-aVerify and repair LaTeX mathematical proofs with adversarial cross-model review.
