Bqo is Pi^1_2-complete

Alberto Marcone

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Bqo is Pi^1_2-complete

Alberto Marcone

Logic · Submitted 24 May 1994

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

The authors' main claim In this paper we prove that the set of countable bqos (viewed as a subset of the Cantor space) is Pi^1_2-complete.

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What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.90 · mentions code or data availability 0.01.

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

In this paper we prove that the set of countable bqos (viewed as a subset of the Cantor space) is Pi^1_2-complete. The notion of bqo or better quasi-ordering arises from combinatorics and is a generalization of the canonical example of a Pi^1_1-complete notion, i.e. that of countable well-ordering. The Pi^1_2-completeness of bqo was conjectured by Clote and proved by the author in his Ph.d. thesis: in this paper we prove it using Simpson's definition of bqo and as little bqo theory as possible.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper we prove that the set of countable bqos (viewed as a subset of the Cantor space) is Pi^1_2-complete.	result 0.86	0.97	0.97	asserted 1.00
s1	The notion of bqo or better quasi-ordering arises from combinatorics and is a generalization of the canonical example of a Pi^1_1-complete notion, i.e. that of countable well-ordering.	background 1.00	0.05	0.03	asserted 1.00
s2	The Pi^1_2-completeness of bqo was conjectured by Clote and proved by the author in his Ph.d. thesis: in this paper we prove it using Simpson's definition of bqo and as little bqo theory as possible.	contribution 0.47	0.85	0.20	asserted 1.00

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Original abstract

In this paper we prove that the set of countable bqos (viewed as a subset of the Cantor space) is Pi^1_2-complete. The notion of bqo or better quasi-ordering arises from combinatorics and is a generalization of the canonical example of a Pi^1_1-complete notion, i.e. that of countable well-ordering. The Pi^1_2-completeness of bqo was conjectured by Clote and proved by the author in his Ph.d. thesis: in this paper we prove it using Simpson's definition of bqo and as little bqo theory as possible.

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