Calliope Ryan-Smith

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20232025

most citedWhich Pairs of Cardinals Can Be Hartogs and Lindenbaum Numbers of a Set?

4 citations · 6 across the 8 of their papers we have counts for

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Showing 2023 · math.LOShow all

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math.LO2023★ 2 cited

The Hartogs-Lindenbaum Spectrum of Symmetric Extensions

Calliope Ryan-Smith

We expand the classic result that $AC_{WO}$ is equivalent to the statement "For all $X$ , $ℵ (X) = ℵ^{*} (X)$ " by proving the equivalence of many more related…

math.LO2023★ 4 cited

Which Pairs of Cardinals Can Be Hartogs and Lindenbaum Numbers of a Set?

Asaf Karagila, Calliope Ryan-Smith

Given any $λ \leq κ$ , we construct a symmetric extension in which there is a set $X$ such that $ℵ (X) = λ$ and $ℵ^{*} (X) = κ$ . Consequently, we show that $ZF +$ "For all pa…

math.LO2023

Stratifiable formulae are not context-free

Calliope Ryan-Smith

Stratified formulae were introduced by Quine as an alternative way to attack Russell's Paradox. Instead of limiting comprehension by size (as in $ZF$ set theory, using its…