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Properties of the Class of Measure Separable Compact Spaces

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Mirna Džamonja, Kenneth Kunen

Logic · Submitted 9 Aug 1994

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

The authors' main claim We show that not being in MS is preserved by all forcing extensions which do not collapse omega_1, while being in MS can be destroyed even by a ccc forcing.

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arXiv IDmath/9408201 (version 1)
Pith IDW2Z4Y3BQ, Pith's permanent record of this paper and its review
CitationKenneth Kunen, Mirna D\v{z}amonja. "Properties of the Class of Measure Separable Compact Spaces." arXiv:math/9408201 (1994). https://pith.science/paper/W2Z4Y3BQ
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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, 4,847 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.52 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.20 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure is equivalent to the existence of a real-valued measurable cardinal less or equal to c. We show that not being in MS is preserved by all forcing extensions which do not collapse omega_1, while being in MS can be destroyed even by a ccc forcing.

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 investigate properties of the class of compact spaces on which every regular Borel measure is separable. contribution 0.96 0.87 0.09 asserted 0.86
s1 This class will be referred to as MS. background 0.73 0.57 0.02 asserted 0.91
s2 We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. contribution 0.57 0.89 0.12 asserted 0.99
s3 Most of the basic theory for regular measures is true just in ZFC. background 0.62 0.17 0.08 asserted 0.98
s4 On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure is equivalent to the existence of a real-valued measurable cardinal less or equal to c. result 0.95 0.39 0.17 asserted 1.00
s5 We show that not being in MS is preserved by all forcing extensions which do not collapse omega_1, while being in MS can be destroyed even by a ccc forcing. result 0.97 0.92 0.27 asserted 1.00

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

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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 investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure is equivalent to the existence of a real-valued measurable cardinal less or equal to c. We show that not being in MS is preserved by all forcing extensions which do not collapse omega_1, while being in MS can be destroyed even by a ccc forcing.

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