id: 01021715
dt: j
an: 01021715
au: Németi, István
ti: Strong representability of fork algebras, a set theoretic foundation.
so: Log. J. IGPL 5, No.1, 3-23 (1997).
py: 1997
pu: Oxford University Press, Oxford
la: EN
cc: 
ut: fork algebra; relation algebra; anti-foundation axiom; representation
    theorem; equational theory; fork operation; finitization problem;
    non-well-founded set theory
ci: 
li: doi:10.1093/jigpal/5.1.3
ab: The aim of the author is to show that there is a particular not
    well-founded set theory (an extension of ZF + AC $-$ Axiom of
    Foundation by a certain anti-foundation axiom) in which a particular
    class of abstract fork algebras defined by finitely many equations
    admits a strong representation theorem: every algebra from the class is
    isomorphic to a set relation algebra with a “concrete” (i.e. set
    theoretically defined) fork operation. This is a refined result, for it
    fails to be provable in more usual set theories or with respect to
    other known variants of concreteness of fork. The author also discusses
    some related results concerning the finitization problem in algebraic
    and in pure first-order logic. The introductory section contains a
    brief history of the subject, with a great many of references.
rv: Jānis Cīrulis (Riga)