Weak theories of concatenation and minimal essentially undecidable theories. An encounter of \(\mathsf{WTC}\) and \(\mathsf{S2S}\)

DOI10.1007/s00153-014-0391-xzbMath1339.03054OpenAlexW1730786771MaRDI QIDQ481870

Kojiro Higuchi, Yoshihiro Horihata

Publication date: 15 December 2014

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-014-0391-x

zbMATH Keywords

interpretabilitytheory of concatenationminimal essentially undecidable theorymonadic second-order theory of two successors

Mathematics Subject Classification ID

Undecidability and degrees of sets of sentences (03D35) Decidability of theories and sets of sentences (03B25) First-order arithmetic and fragments (03F30) Gödel numberings and issues of incompleteness (03F40) Relative consistency and interpretations (03F25)

Related Items (6)

MUTUAL INTERPRETABILITY OF WEAK ESSENTIALLY UNDECIDABLE THEORIES ⋮ First-order concatenation theory with bounded quantifiers ⋮ CURRENT RESEARCH ON GÖDEL’S INCOMPLETENESS THEOREMS ⋮ FINDING THE LIMIT OF INCOMPLETENESS I ⋮ Weak essentially undecidable theories of concatenation ⋮ On interpretability between some weak essentially undecidable theories

Cites Work

• Weak theories of concatenation and arithmetic
• Decidability without mathematics
• Growing commas. A study of sequentiality and concatenation
• On interpretability in the theory of concatenation
• Undecidability without arithmetization
• Undecidable theories
• Arithmetic on semigroups
• Variants of Robinson's essentially undecidable theoryR
• Decidability of Second-Order Theories and Automata on Infinite Trees
• Concatenation as a basis for arithmetic
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