7 papers · 1 filter
Upwards homogeneity in iterated symmetric extensions
Calliope Ryan-Smith, Jonathan Schilhan, Yujun Wei
It is sometimes desirable in choiceless constructions of set theory that one iteratively extends some ground model without adding new sets of ordinals after the first extension. Pu…
Eccentricity, extendable choice and descending distributive forcing
Calliope Ryan-Smith
We introduce the forcing property of descending distributivity. A forcing is -descending distributive if for all decreasing sequences of open dens…
Local reflections of choice
Calliope Ryan-Smith
Under the assumption of small violations of choice with seed (), the failure of many choice principles reflect to to local properties of , which can be a he…
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 set theory, using its…
Proper classes of maximal -independent families from large cardinals
Calliope Ryan-Smith
While maximal independent families can be constructed from ZFC via Zorn's lemma, the presence of a maximal -independent family already gives an inner model with a measurable ca…
The Hartogs-Lindenbaum Spectrum of Symmetric Extensions
Calliope Ryan-Smith
We expand the classic result that is equivalent to the statement "For all , " by proving the equivalence of many more related…