On Preservation Theorems for Two‐Variable Logic | Zendy

Gradel Erich | Zendy; Rosen Eric | Zendy

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On Preservation Theorems for Two‐Variable Logic

Author(s) -

Gradel Erich,

Rosen Eric

Publication year - 1999

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19990450304

Subject(s) - mathematics , homomorphism , variable (mathematics) , discrete mathematics , second order logic , order (exchange) , pure mathematics , higher order logic , computer science , theoretical computer science , mathematical analysis , description logic , finance , economics

We show that the existential preservation theorem fails for two‐variable first‐order logic FO 2 . It is known that for all k ≥ 3, FO k does not have an existential preservation theorem, so this settles the last open case, answering a question of Andreka, van Benthem, and Németi. In contrast, we prove that the homomorphism preservation theorem holds for FO 2 .

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