y = 2x VS. y = 3x

y = 2x VS. y = 3x

We show that no formula of first order logic using linear ordering and the logical relation y = 2x can define the property that the size of a finite model is divisible by 3. This answers a long-standing question which may be of relevance to certain open problems in circuit complexity.

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Veröffentlicht in:The Journal of symbolic logic 1997-06, Vol.62 (2), p.661-672
Hauptverfasser: Stolboushkin, Alexei, Niwiński, Damian
Format: Artikel
Sprache:eng
Schlagworte:
Cardinality
Games
Logical theorems
Model theory
Natural numbers
Pebbles
Plant roots
Predicate logic
Predicates
Signatures
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Beschreibung
Zusammenfassung:We show that no formula of first order logic using linear ordering and the logical relation y = 2x can define the property that the size of a finite model is divisible by 3. This answers a long-standing question which may be of relevance to certain open problems in circuit complexity.
ISSN:0022-4812
1943-5886
DOI:10.2307/2275554