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The ordered field of real numbers and logics with Malitz quantifiers

Journal of Symbolic Logic 50 (2):380-389 (1985)

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TheL <ω-theory of the class of Archimedian real closed fields.Gerd Bürger - 1989 - Archive for Mathematical Logic 28 (3):155-166.details For the classA of uncountable Archimedian real closed fields we show that the statement “TheL <ω-theory ofA is complete” is independent of ZFC. In particular we have the following results:Assuming the Continuum-Hypothesis (CH) is incomplete. Conversely it is possible to build a model of set theory in which is complete and decidable. The latter can also be deduced from the Proper Forcing Axiom (PFA). In this case turns out to be equivalent to the elementary theory of the real numbers ℝ (...) Download Export citation Bookmark 1 citation
An Application of Logic to Combinatorial Geometry: How Many Tetrahedra are Equidecomposable with a Cube?Vladik Kreinovich & Olga Kosheleva - 1994 - Mathematical Logic Quarterly 40 (1):31-34.details The main result of this paper were announced in Kosheleva — Kreinovich [7, 8]; for other algorithmic aspects of Hilbert's Third Problem see Kosheleva [6]. The authors are greatly thankful to Alexandr D. Alexandrov , Vladimir G. Boltianskii and Patrick Suppes for valuable discussions, and to the anonymous referee for important suggestions. This work was partially supported by an NSF grant No. CDA-9015006. Download Export citation Bookmark
On the elimination of Malitz quantifiers over Archimedian real closed fields.Peter Koepke - 1989 - Archive for Mathematical Logic 28 (3):167-171.details Download Export citation Bookmark

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