A geometric iteration method is developed for generalised perfect set forcing P(F), enabling its iteration with ≤κ supports along well-founded partial orders while preserving cardinals ≤κ⁺.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Ramsey theory of block sequences in infinite-dimensional discrete vector spaces is parametrized by perfect sets, proving dichotomies for definable families of partitions and linear transformations while examining preservation of selective ultrafilter analogues under Sacks forcing.
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Iterating Generalised Perfect Set Forcing Along Well-Founded Orders
A geometric iteration method is developed for generalised perfect set forcing P(F), enabling its iteration with ≤κ supports along well-founded partial orders while preserving cardinals ≤κ⁺.
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Parametrizing the Ramsey theory of vector spaces I: Discrete spaces
Ramsey theory of block sequences in infinite-dimensional discrete vector spaces is parametrized by perfect sets, proving dichotomies for definable families of partitions and linear transformations while examining preservation of selective ultrafilter analogues under Sacks forcing.