First-order logics of quasiary predicates

Shkilniak, S.S.

doi:10.1007/s10559-010-9270-6

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2021

Publication Types

Select...

Article1

Other1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 4 publications

(3 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Undecidability of the Logic of Partial Quasiary Predicates

Rybakov

Shkatov

2021

Logic Journal of the IGPL

View full text Add to dashboard Cite

We obtain an effective embedding of the classical predicate logic into the logic of partial quasiary predicates. The embedding has the property that an image of a non-theorem of the classical logic is refutable in a model of the logic of partial quasiary predicates that has the same cardinality as the classical countermodel of the non-theorem. Therefore, we also obtain an embedding of the classical predicate logic of finite models into the logic of partial quasiary predicates over finite structures. As a consequence, we prove that the logic of partial quasiary predicates is undecidable—more precisely, $\varSigma ^0_1$-complete—over arbitrary structures and not recursively enumerable—more precisely, $\varPi ^0_1$-complete—over finite structures.

show abstract