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What properties of numbers are needed to model accelerated observers in relativity?

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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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Gergely Székely

Logic · Submitted 29 Sep 2012

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

The authors' main claim Consequently, the class of fields over which uniform acceleration can be investigated is not axiomatizable in the language of ordered fields.

how it is stated · asserted 1.00 read the record →

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arXiv ID1210.0101 (version 1)
Pith IDR2VRJ4N4, Pith's permanent record of this paper and its review
CitationGergely Sz\'ekely. "What properties of numbers are needed to model accelerated observers in relativity?." arXiv:1210.0101 (2012). https://pith.science/paper/R2VRJ4N4
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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,585 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.86 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.14 · 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 the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every real closed field. We also show that, if we would like to model certain accelerated observers, then not every real closed field is suitable, e.g., uniformly accelerated observers cannot be modeled over the field of real algebraic numbers. Consequently, the class of fields over which uniform acceleration can be investigated is not axiomatizable in the language of ordered fields.

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 the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. contribution 0.65 0.82 0.04 unclear 0.36
s1 We present a general axiomatic theory of accelerated observers which has a model over every real closed field. contribution 0.64 0.94 0.18 asserted 1.00
s2 We also show that, if we would like to model certain accelerated observers, then not every real closed field is suitable, e.g., uniformly accelerated observers cannot be modeled over the field of real algebraic numbers. result 0.97 0.93 0.26 asserted 0.97
s3 Consequently, the class of fields over which uniform acceleration can be investigated is not axiomatizable in the language of ordered fields. result 0.60 0.89 0.53 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 investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every real closed field. We also show that, if we would like to model certain accelerated observers, then not every real closed field is suitable, e.g., uniformly accelerated observers cannot be modeled over the field of real algebraic numbers. Consequently, the class of fields over which uniform acceleration can be investigated is not axiomatizable in the language of ordered fields.

Human review

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1 arXiv paper cite this in 1 sentence

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

What it cites · 9 sentences without a confident label

Cites as background 1 paper

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