EXPANSIONS OF THE ORDERED ADDITIVE GROUP OF REAL NUMBERS BY TWO DISCRETE SUBGROUPS

DOI10.1017/jsl.2015.34zbMath1436.03208arXiv1407.7002OpenAlexW2962760733MaRDI QIDQ2976377

Philipp Hieronymi

Publication date: 28 April 2017

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.7002

zbMATH Keywords

decidabilityOstrowski numeration systemmonadic second order logic of one successorordered additive group of real numbers

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Automata and formal grammars in connection with logical questions (03D05) Decidability of theories and sets of sentences (03B25) Model theory of ordered structures; o-minimality (03C64)

Related Items (7)

Interpreting the monadic second order theory of one successor in expansions of the real line ⋮ A wild model of linear arithmetic and discretely ordered modules ⋮ The additive structure of integers with the lower Wythoff sequence ⋮ Ostrowski numeration systems, addition, and finite automata ⋮ A tetrachotomy for expansions of the real ordered additive group ⋮ When is scalar multiplication decidable? ⋮ Unnamed Item

Cites Work

• Logical number theory I. An introduction
• The theory of \(\langle \mathbb{N} , +, V_ k, V_ l\rangle\) is undecidable
• Interpreting the projective hierarchy in expansions of the real line
• Defining the set of integers in expansions of the real field by a closed discrete set
• Representations of numbers and finite automata
• Automata theory and its applications

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