Forcing in the alternative set theory. II

Jiří Sgall; Antonín Sochor

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 339-353
  • ISSN: 0010-2628

Abstract

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By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice.

How to cite

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Sgall, Jiří, and Sochor, Antonín. "Forcing in the alternative set theory. II." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 339-353. <http://eudml.org/doc/247246>.

@article{Sgall1991,
abstract = {By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice.},
author = {Sgall, Jiří, Sochor, Antonín},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {alternative set theory; second order arithmetic; forcing; schemes of choice; axiom of constructibility; degrees of constructibility; alternative set theory; forcing; axiom of constructibility; degrees of constructibility; metamathematical problems of AST; higher-order arithmetics; schemes of choice for classes},
language = {eng},
number = {2},
pages = {339-353},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Forcing in the alternative set theory. II},
url = {http://eudml.org/doc/247246},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Sgall, Jiří
AU - Sochor, Antonín
TI - Forcing in the alternative set theory. II
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 339
EP - 353
AB - By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice.
LA - eng
KW - alternative set theory; second order arithmetic; forcing; schemes of choice; axiom of constructibility; degrees of constructibility; alternative set theory; forcing; axiom of constructibility; degrees of constructibility; metamathematical problems of AST; higher-order arithmetics; schemes of choice for classes
UR - http://eudml.org/doc/247246
ER -

References

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  1. Adamowicz Z., Constructible semi-lattices of degrees of constructibility, In: Set Theory and Hierarchy Theory V, Lecture Notes in Mathematics 619, p. 1-43. Zbl0369.02042MR0505487
  2. Lévy A., Definability in axiomatic set theory II, In: Mathematical Logic and Foundations of Set Theory, ed. by Y. Bar-Hillel, North-Holland, 1970. MR0268037
  3. Sochor A., Metamathematics of the alternative set theory II, Comment. Math. Univ. Carolinae 23 (1982), 55-79. (1982) Zbl0493.03030MR0653351
  4. Sochor A., Constructibility and shiftings of view, Comment. Math. Univ. Carolinae 26 (1985), 477-498. (1985) Zbl0583.03040MR0817822
  5. Sgall J., Forcing in the alternative set theory I, Comment. Math. Univ. Carolinae 32 (1991), 323-337. (1991) Zbl0751.03025MR1137794
  6. Vopěnka P., Mathematics in the Alternative Set Theory, Leipzig, 1979. MR0581368

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