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The monadic theory of order

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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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Saharon Shelah

Logic · Submitted 1 May 2023

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

The authors' main claim We prove (CH) that the monadic theory of the real order is undecidable.

how it is stated · asserted 0.98 read the record →

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arXiv ID2305.00968 (version 1)
Pith IDPFJUKDEY, Pith's permanent record of this paper and its review
CitationSaharon Shelah. "The monadic theory of order." arXiv:2305.00968 (2023). https://pith.science/paper/PFJUKDEY
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,065 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.84 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.72 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We deal with the monadic (second-order) theory of order. We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. We prove (CH) that the monadic theory of the real order is undecidable. Our methods are model-theoretic, and we do not use automaton theory. This is a slightly corrected version of a very old work.

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 deal with the monadic (second-order) theory of order. background 0.91 0.45 0.03 asserted 0.81
s1 We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. contribution 1.00 0.93 0.16 asserted 1.00
s2 We prove (CH) that the monadic theory of the real order is undecidable. result 0.97 0.92 0.55 asserted 0.98
s3 Our methods are model-theoretic, and we do not use automaton theory. method 0.99 0.83 0.03 asserted 1.00
s4 This is a slightly corrected version of a very old work. background 0.97 0.32 0.02 asserted 1.00

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
levels run
  • 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 deal with the monadic (second-order) theory of order. We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. We prove (CH) that the monadic theory of the real order is undecidable. Our methods are model-theoretic, and we do not use automaton theory. This is a slightly corrected version of a very old work.

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