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Intensional solutions to the identity problem for partial sets

Hinion R.

Reports on Mathematical Logic

2007

No. 42

47-69

A general forcing method is developed that allows to construct pure term models for (roughly speaking) predicative first-order partial set theory, where specific identification/differentiation rules hold. The applications bring new results about the links with intensionality and extensionality.

Intensional positive set theory

Hinion R.

Reports on Mathematical Logic

2006

Nr 40

107-125

This paper shows that, via a simple kind of forcing, one can construct a pure term model for intensional positive set theory, where sets are defined by positive formulas and identifica- tions are ruled by equivalence of the defining formulas. Further one can also construct a model that "contains ZF".