Frank Gilson

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math.LO2025

Arithmetical Complexity and Absoluteness of Rigidity Phenomena for Ulam Sequences

Frank Gilson

We analyse the logical complexity and absoluteness of natural statements about Ulam sequences, with particular emphasis on the rigidity phenomena introduced by Hinman, Kuca, Schles…

math.LO2025

From Internal to External: Classical Models of ZF + PP + $\neg$ AC

Frank Gilson

Goal. We analyze when the Partition Principle ( $PP$ ) holds without $AC$ in models arising from a free finite $H$ -action on Cantor space, and reconcile two standar…

math.LO2025

Symmetric Iterations with Countable and $< κ$ -Support: A Framework for Choiceless ZF Extensions

Frank Gilson

We develop a unified framework for iterated symmetric extensions with countable support and, more generally, with $< κ$ -support. Set-length iterations are treated uniformly, and whe…

math.LO2025

Partition Principle without Choice via Symmetric Iterations and Sheaf-Toposes

Frank Gilson

We study the topos $E = Sh (H ⋉ 2^{N})$ arising from a nontrivial finite group $H$ acting freely on Cantor space. Using a local embedding property for…

Arithmetical Complexity and Absoluteness of Rigidity Phenomena for Ulam Sequences

From Internal to External: Classical Models of ZF + PP + ¬AC

Symmetric Iterations with Countable and <κ-Support: A Framework for Choiceless ZF Extensions

Partition Principle without Choice via Symmetric Iterations and Sheaf-Toposes

From Internal to External: Classical Models of ZF + PP + $\neg$ AC

Symmetric Iterations with Countable and $< κ$ -Support: A Framework for Choiceless ZF Extensions