# Measurable cardinals and good -wellorderings

@article{Lcke2018MeasurableCA, title={Measurable cardinals and good -wellorderings}, author={Philipp L{\"u}cke and Philipp Schlicht}, journal={Math. Log. Q.}, year={2018}, volume={64}, pages={207-217} }

We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals κ with the property that the collection of all initial segments of the wellordering is definable by a Σ1-formula with parameter κ. A short argument shows that the existence of a measurable cardinal δ implies that such wellorderings do not exist at δ-inaccessible cardinals of cofinality not equal to δ and their successors. In contrast, our main result shows that these…

## 5 Citations

$\Sigma_1$-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders

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Given an uncountable cardinal κ, we consider the question whether subsets of the power set of κ that are usually constructed with the help of the Axiom of Choice are definable by Σ1-formulas that…

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We investigate the relation betweenC∗, themodel of sets constructible using first order logic augmented with the “cofinality-ω” quantifier, and “short” sequences of measures – sequences of measures…

CLOSURE PROPERTIES OF MEASURABLE ULTRAPOWERS

- Mathematics
- 2020

We study closure properties of measurable ultrapowers with respect to Hamkin’s notion of freshness and show that the extent of these properties highly depends on the combinatorial properties of the…

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