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Canonization of analytic equivalences on the Carlson-Simpson forcing

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Michal Doucha

Logic · Submitted 10 Apr 2013

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

The authors' main claim We prove a canonization result for the Carlson-Simpson forcing in the spirit of \cite{KSZ}.

how it is stated · asserted 1.00 read the record →

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arXiv ID1304.3019 (version 1)
Pith IDEEKB5NQO, Pith's permanent record of this paper and its review
CitationMichal Doucha. "Canonization of analytic equivalences on the Carlson-Simpson forcing." arXiv:1304.3019 (2013). https://pith.science/paper/EEKB5NQO
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The compiled record

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,380 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We prove a canonization result for the Carlson-Simpson forcing in the spirit of \cite{KSZ}. We generalize the weak form of the Carlson-Simpson theorem (\cite{CaSi}) dealing with partitions without free blocks: instead of dealing with finite Borel (resp. Baire-property) colorings we deal with (uncountable) colorings such that the corresponding equivalence relation (two partitions are equivalent if they are colored by the same color) is analytic.

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 a canonization result for the Carlson-Simpson forcing in the spirit of \cite{KSZ}. result 0.57 0.95 0.74 asserted 1.00
s1 We generalize the weak form of the Carlson-Simpson theorem (\cite{CaSi}) dealing with partitions without free blocks: instead of dealing with finite Borel (resp. Baire-property) colorings we deal with (uncountable) colorings such that the corresponding equivalence relation (two partitions are equivalent if they are colored by the same color) is analytic. contribution 0.96 0.88 0.58 asserted 0.98

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

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 a canonization result for the Carlson-Simpson forcing in the spirit of \cite{KSZ}. We generalize the weak form of the Carlson-Simpson theorem (\cite{CaSi}) dealing with partitions without free blocks: instead of dealing with finite Borel (resp. Baire-property) colorings we deal with (uncountable) colorings such that the corresponding equivalence relation (two partitions are equivalent if they are colored by the same color) is analytic.

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1 arXiv paper cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Compares with it 1 paper
  • Indeed, Proposition [ref] illustrates that Theorem [ref] cannot be attained by the “mutual generics" technique for (reduced) product forcings that was used in [ref] and [ref] ; finer techniques designed specifically for CBERs are necessary.

    Every CBER is smooth below the Carlson-Simpson generic partition · Main results · 0.97

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