9 papers
A countable-support symmetric iteration separating PP from AC
Frank Gilson
We construct, from a ground model of , a transitive symmetric model satisfying . The construction starts with a Cohen symmetric seed mode…
The Modal Logic of Finitely Symmetry-Preserving Iterated Extensions is Exactly S4
Frank Gilson
We determine the ZF-provable modal logic of the modality , where means ' holds in every finite symmetry-preserving iteration' of th…
A One-Step Cascade Symmetric Model: Rank- Packets, Binary Shielding, and the Even Exact-Cardinality Profile
Frank Gilson
We introduce a one-step cascade symmetric system whose local symmetry geometry is organized by finite -closed windows and one-step stars rather than by rowwise-independent togg…
Limit Filters and Dependent Choice in Countable-Support Symmetric Iterations
Frank Gilson
We isolate the limit-stage filter construction needed for countable-support symmetric iterations built from standard successor-step symmetric systems. At successor stages we take t…
Explicit separation of quadratic irrationals from the middle-third Cantor set
Frank Gilson
Assuming a mild non-degeneracy condition excluding very low-level Cantor endpoints, and assuming a counting/input hypothesis for the contribution of non-deep orbit indices, we show…
From Internal to External: Classical Models of ZF + PP + AC
Frank Gilson
Goal. We analyze when the Partition Principle () holds without in models arising from a free finite -action on Cantor space, and reconcile two standar…