# Measurability Properties on Small Cardinals

@inproceedings{Eskew2014MeasurabilityPO, title={Measurability Properties on Small Cardinals}, author={Monroe Eskew}, year={2014} }

Author(s): Eskew, Monroe Blake | Advisor(s): Zeman, Martin | Abstract: Ulam proved that there cannot exist a probability measure on the reals for which every set is measurable and gets either measure zero or one. He asked how large a collection of partial 0-1 valued measures is required so that every set of reals is measurable in one of them. Alaoglu and Erdos proved that if the continuum hypothesis holds, then countably many measures is not enough, and Ulam asked if aleph_1 many can suffice…

## 6 Citations

### Prikry-type forcings after collapsing a huge cardinal

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. Some models of combinatorial principles have been obtained by collapsing a huge cardinal in the case of the successors of regular cardinals. For example, saturated ideals, Chang’s conjecture,…

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### Nonregular ideals

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Most of the regularity properties of ideals introduced by Taylor are equivalent at successor cardinals. For $\kappa = \mu^+$ with $\mathrm{cf}(\mu)$ uncountable, we can rid the universe of dense…

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James Earl Baumgartner (March 23, 1943 – December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the…

### Some mutually inconsistent generic large cardinals

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Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.

### In memoriam: James Earl Baumgartner (1943–2011)

- MathematicsArch. Math. Log.
- 2017

James Earl Baumgartner came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done.

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