Models and Satisfiability

Grzegorz Bancerek

Warsaw University, Bialystok

Supported by RPBP.III-24.C1.

Summary.

The article includes schemes of defining by structural induction, and definitions and theorems related to: the set of variables which have free occurrences in a ZF-formula, the set of all valuations of variables in a model, the set of all valuations which satisfy a ZF-formula in a model, the satisfiability of a ZF-formula in a model by a valuation, the validity of a ZF-formula in a model, the axioms of ZF-language, the model of the ZF set theory.

MML Identifier: ZF_MODEL

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. A model of ZF set theory language. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[5] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[6] Andrzej Trybulec. Enumerated sets. Journal of Formalized Mathematics, 1, 1989.

[7] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[9] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.