Farmer Schlutzenberg

collaborators

3 papers

math.LO2024

Ladder mice

Assume ZF + AD + $V = L (R)$ . We prove some "mouse set" theorems, for definability over $J_{α} (R)$ where $[α, α]$ is a projective-like gap (of $L (R)$ ) and $α$ …

math.LO2024

Stationary tower free homogeneously Suslin scales

Farmer Schlutzenberg, John R. Steel

Let $λ$ be a limit of Woodin cardinals. It was shown by the second author that the pointclass of $< λ$ -homogeneously Suslin sets has the scale property. We give a new proof of thi…

math.LO2024

Mice with Woodin cardinals from a Reinhardt

Farmer Schlutzenberg

Suppose there is a Reinhardt cardinal. Then (1) $M_{n} (X)$ exists and is fully iterable (above $X$ ) for every transitive set $X$ and every $n < ω$ (here $M_{n} (X)$ denotes the canonical…