DEF0115canonicalv1Cylinder Domain
A subset of tau^3 expressible as a finite Boolean combination of stage-k cylinders. The cylinder domains form the Boolean algebra generated by {C_k(x)}.
Payload
Cylinder Domain
A subset of tau^3 expressible as a finite Boolean combination of stage-k cylinders. The cylinder domains form the Boolean algebra generated by {C_k(x)}.
Cylinder Domain
Summary
A subset of tau^3 expressible as a finite Boolean combination of stage-k cylinders. The cylinder domains form the Boolean algebra generated by {C_k(x)}.
Statement
%
\label{def:cylinder-domain}
A \textbf{cylinder domain} in~$\tau^3$
is any subset that can be expressed
as a finite Boolean combination
(union, intersection, complement)
of stage-$k$ cylinders.
That is, the cylinder domains form
the Boolean algebra generated by
$\{C_k(x) : k \geq 1,\; x \in \tau^3\}$.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-02.jsonlline 19 - Manuscript source:
2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part02/ch09-cylinder-domains.texlines 196-207
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookII.Domains.Cylinders - Name:
cylinder_mem
Dependencies
- Canonical: I.T18, II.D02
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
II.D09cylinder-domaindef:cylinder-domainRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.