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Contributions to the theory of semisets V: On the axiom of general collapse

✍ Scribed by Petr Vopênka; Antonín Sochor

Publisher
John Wiley and Sons
Year
1975
Tongue
English
Weight
1019 KB
Volume
21
Category
Article
ISSN
0044-3050

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✦ Synopsis

CONTRIBUTIONS TO THE THEORY OF SEMISETS V On the axiom of general collapse

In the article we prove the consistency of some important axioms of the theory of scwiisets (TSS). The method we use differs from the method of [ll] since in [113 the basic model is the ultraproduct and here it is the model described in 1121. This approach enables us to eliminate the axiom of choice from our considerations and, moreover, enables us to prove consistency statements that we can hardly prove using the ultraproduct model. It must be noticed that we shall deal with consistency of theories which cannot be extended to set theory.

In (3505 we formulate two theoriesthe collapsing non-standard theory of semisets and the collapsing standard theory of semisets. On the one hand these theories

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