Skip to Main content Skip to Navigation
Journal articles

Spectra and satisfiability for logics with successor and a unary func- tion

Abstract : We investigate the expressive power of two logics, both with the successor function: first-order logic with an un-interpreted function, and existential monadic second order logic — that is first-order logic over words —, with multiplication by a constant b. We prove that all b-recognizable sets are spectra of those logics. Furthermore, it is proven that some encoding of the set of halting times of a non-deterministic 2-counter automaton is also a spectrum. This yields undecidability of the finite satisfiability problem for those logics. Finally, it is shown that first-order logic with one uninterpreted function and successor can encode quickly increasing functions, such as the Knuth's up-arrows.
Document type :
Journal articles
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download
Contributor : Arthur Milchior Connect in order to contact the contributor
Submitted on : Saturday, January 6, 2018 - 6:00:29 AM
Last modification on : Tuesday, October 19, 2021 - 4:09:40 PM
Long-term archiving on: : Saturday, April 7, 2018 - 12:32:28 PM


Files produced by the author(s)


  • HAL Id : hal-01676718, version 1


Arthur Milchior. Spectra and satisfiability for logics with successor and a unary func- tion. Mathematical Logic Quarterly, Wiley, In press. ⟨hal-01676718⟩



Record views


Files downloads