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A Galvin–Hajnal theorem for generalized cardinal characteristics
We prove that a variety of generalized cardinal characteristics, including meeting numbers, the rea** number, and the dominating number, satisfy an...
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On strong algebrability of families of non-measurable functions of two variables
Recently Tomasz Natkaniec in (Natkaniec in Rev R Acad Cenc Exactas Fís Nat Ser A Mat RACSAM, 115(1):10, 2021) studied the lineability problem for...
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On minimax cardinal spline interpolation
It is shown that in the problem of cardinal interpolation, spline interpolants of various degrees are R -minimax, with respect to corresponding...
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Forcing level by level equivalence and a consequence of UA
We show how Hamkins’ Gap Forcing Theorem of Hamkins (Israel J Math 125:237–252, 2001, Bull Symb Logic 5: 264–272, 1999) can be used to give an...
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Lower consistency bounds for mutual stationarity with divergent cofinalities and limited covering
We improve previous work on the consistency strength of mutually stationary sequences of sets concentrating on points with divergent cofinality...
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Distributivity and minimality in perfect tree forcings for singular cardinals
Dobrinen, Hathaway and Prikry studied a forcing ℙ κ consisting of perfect trees of height λ and width κ where κ is a singular λ-strong limit of...
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Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
In this series of papers we advance Ramsey theory over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and...
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Hanf numbers for extendibility and related phenomena
This paper contains portions of Baldwin’s talk at the Set Theory and Model Theory Conference (Institute for Research in Fundamental Sciences, Tehran,...
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Perfect subtree property for weakly compact cardinals
We investigate the consistency strength of the statement: κ is weakly compact and there is no tree on κ with exactly κ + many branches. We show that...
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Coneability of Anti-Fubini Functions and Other Lineability Properties
It is proved that the family of measurable real functions on the product measure space satisfying (or not) the conclusion of Fubini’s Theorem (along...
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Reflection principles, GCH and the uniformization properties
Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties,...
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