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5 papers · 1 filter
Combinatorial properties of Hechler forcing
Jörg Brendle, Haim Judah, Saharon Shelah
In this work we use a notion of rank first introduced by James Baumgartner and Peter Dordal and later developed independently by the third author to show that adding a Hechler real…
Baire property and Axiom of Choice
Haim Judah, Saharon Shelah
We show that (1) If ZF is consistent then the following theory is consistent "ZF + DC(omega_{1}) + Every set of reals has Baire property" and (2) If ZF is consistent then the follo…
Amoeba-absoluteness and projective measurability
Jörg Brendle
We study the relationship between Amoeba forcing (the partial order which generically adds a measure one set of random reals) and projective measurability. Given a universe V of se…
Perfect sets of random reals
Jörg Brendle, Haim Judah
We discuss the relationship between perfect sets of random reals, dominating reals, and the product of two copies of the random algebra B. Recall that B is the algebra of Borel set…
Many simple cardinal invariants
Martin Goldstern, Saharon Shelah
For g < f in omega^omega we define c(f,g) be the least number of uniform trees with g-splitting needed to cover a uniform tree with f-splitting. We show that we can simultaneously…