Independently Axiomatizable L_{omega_1,omega} Theories

Details Independently Axiomatizable L_{omega_1,omega} Theories Independently Axiomatizable L_{omega_1,omega} Theories

2010-12-15

arxiv.org/abs/1012.3422v1

G. Hjorth, I. Souldatos, Independently axiomatizable $L_{\omega _{1},\omega}$ theories, J. Symbolic Logic, Volume 74, Issue 4

Mathematics

Logic

16 pages, no figures

Scientific paper

10.2178/jsl/1254748691

In partial answer to a question posed by Arnie Miller (http://www.math.wisc.edu/~miller/res/problem.pdf) and X. Caicedo, we obtain sufficient conditions for an L_{omega_1,omega} theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every L_{omega_1,omega} theory in a countable language has an independent axiomatization. The second, this time outright in ZFC, every intersection of a family of Borel sets can be formed as the intersection of a family of independent Borel sets.

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