en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9890)

2014-02-01T06:44:57Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9890)

New page

In [[mathematical logic]], the '''Barwise compactness theorem''', named after [[Jon Barwise]], is a generalization of the usual [[compactness theorem]] for [[first-order logic]] to a certain class of infinitary languages. It was stated and proved by Barwise in 1967.

==Statement of the theorem==

Let <math>A</math> be a countable [[admissible set]]. Let <math>L</math> be an <math>A</math>-finite relational language. Suppose <math>\Gamma</math> is a set of <math>L_A</math>-sentences, where <math>\Gamma</math> is a <math>\Sigma_1</math> set with parameters from <math>A</math>, and every <math>A</math>-finite subset of <math>\Gamma</math> is satisfiable. Then <math>\Gamma</math> is satisfiable.

==References==
*{{ cite book | title=Infinitary Logic and Admissible Sets (Ph. D. Thesis) | author=Barwise, J. | publisher=Stanford University| year=1967}}
* {{cite book | title=Computable Structures and the Hyperarithmetic Hierarchy | author=C. J. Ash | coauthors=Knight, J. | publisher=[[Elsevier]] | year=2000 | isbn=0-444-50072-3 | pages=366 }}
* {{cite book | title=Model-theoretic logics | author=Jon Barwise | coauthors=Solomon Feferman, John T. Baldwin | publisher=[[Springer-Verlag]] | year=1985 | isbn=3-540-90936-2 | pages=295 }}

==External links==
* [http://plato.stanford.edu/entries/logic-infinitary/#5] ''Stanford Encyclopedia of Philosophy'', "Infinitary Logic", Section 5, "Sublanguages of L(ω1,ω) and the Barwise Compactness Theorem"

[[Category:Theorems in the foundations of mathematics]]
[[Category:Mathematical logic]]
[[Category:Metatheorems]]

{{mathlogic-stub}}

Critical field - Revision history

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9890)