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On $\omega$-Strongly Measurable Cardinals

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Omer Ben-Neria, Yair Hayut

Logic · Submitted 11 Nov 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa) = \kappa$, that every successor of a regular cardinal is $\omega$-strongly measurable in HOD.

how it is stated · asserted 0.50 read the record →

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arXiv ID1911.04568 (version 5)
Pith ID3PSYYSGK, Pith's permanent record of this paper and its review
CitationOmer Ben-Neria, Yair Hayut. "On $\omega$-Strongly Measurable Cardinals." arXiv:1911.04568 (2019). https://pith.science/paper/3PSYYSGK
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,296 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.40 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; .

We prove several consistency results concerning the notion of $\omega$-strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa) = \kappa$, that every successor of a regular cardinal is $\omega$-strongly measurable in HOD.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove several consistency results concerning the notion of $\omega$-strongly measurable cardinal in HOD. contribution 0.94 0.95 0.36 asserted 1.00
s1 In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa) = \kappa$, that every successor of a regular cardinal is $\omega$-strongly measurable in HOD. result 0.98 0.94 0.64 asserted 0.50

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We prove several consistency results concerning the notion of $\omega$-strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa) = \kappa$, that every successor of a regular cardinal is $\omega$-strongly measurable in HOD.

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