Archive for Mathematical Logic 51 (3-4):353-371 (2012)

Abstract
A theory of two-sided containers, denoted ZF2, is introduced. This theory is then shown to be synonymous to ZF in the sense of Visser (2006), via an interpretation involving Quine pairs. Several subtheories of ZF2, and their relationships with ZF, are also examined. We include a short discussion of permutation models (in the sense of Rieger–Bernays) over ZF2. We close with highlighting some areas for future research, mostly motivated by the need to understand non-wellfounded games
Keywords Set theory  Combinatorial game theory  Interpretations
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DOI 10.1007/s00153-012-0275-x
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References found in this work BETA

On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
On Ordered Pairs.W. V. Quine - 1945 - Journal of Symbolic Logic 10 (3):95-96.
A Note on Recursive Models of Set Theories.Domenico Zambella & Antonella Mancini - 2001 - Notre Dame Journal of Formal Logic 42 (2):109-115.

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