Journal of Symbolic Logic

Expressing cardinality quantifiers in monadic second-order logic over chains

Vince Bárány, łukasz Kaiser, and Alexander Rabinovich

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Abstract

We investigate the extension of monadic second-order logic of order with cardinality quantifiers “there exists uncountably many sets such that …” and “there exists continuum many sets such that …”. We prove that over the class of countable linear orders the two quantifiers are equivalent and can be effectively and uniformly eliminated. Weaker or partial elimination results are obtained for certain wider classes of chains. In particular, we show that over the class of ordinals the uncountability quantifier can be effectively and uniformly eliminated. Our argument makes use of Shelah's composition method and Ramsey-like theorem for dense linear orders.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 2 (2011), 603-619.

Dates
First available in Project Euclid: 19 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1305810766

Digital Object Identifier
doi:10.2178/jsl/1305810766

Mathematical Reviews number (MathSciNet)
MR2830418

Zentralblatt MATH identifier
1222.03009

Citation

Bárány, Vince; Kaiser, łukasz; Rabinovich, Alexander. Expressing cardinality quantifiers in monadic second-order logic over chains. J. Symbolic Logic 76 (2011), no. 2, 603--619. doi:10.2178/jsl/1305810766. https://projecteuclid.org/euclid.jsl/1305810766


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