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Algebra Logika, 2004, Volume 43, Number 6, Pages 749–758 (Mi al109)  

The Löwenheim–Skolem–Mal'tsev Theorem for $\mathbb{HF}$-Structures

V. G. Puzarenko

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We deal with the problem asking whether hereditarily finite superstructures have elementary extensions of the form $\mathbb{HF}(\mathfrak M)$. In so doing, we settle the question whether a theory for some hereditarily finite superstructure have $\mathbb{HF}(\mathfrak M)$ models of arbitrarily large cardinality. A Hanf number is shown to exist, and we provide an exact bound for the countable case.

Keywords: hereditarily finite superstructure, Hanf number

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English version:
Algebra and Logic, 2004, 43:6, 418–423

Bibliographic databases:

UDC: 510.5
Received: 18.09.2002

Citation: V. G. Puzarenko, “The Löwenheim–Skolem–Mal'tsev Theorem for $\mathbb{HF}$-Structures”, Algebra Logika, 43:6 (2004), 749–758; Algebra and Logic, 43:6 (2004), 418–423

Citation in format AMSBIB
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\by V.~G.~Puzarenko
\paper The L\"{o}wenheim--Skolem--Mal'tsev Theorem for $\mathbb{HF}$-Structures
\jour Algebra Logika
\yr 2004
\vol 43
\issue 6
\pages 749--758
\mathnet{http://mi.mathnet.ru/al109}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2135390}
\zmath{https://zbmath.org/?q=an:1097.03024}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 6
\pages 418--423
\crossref{https://doi.org/10.1023/B:ALLO.0000048830.64509.c7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249091930}


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